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1. 6 10 Actions Retrieve Series This command adds items such as residuals fitted values conditional variances switch probabilities and other generated series to the data set To use it first open the Options Output and Retrieval dialog and check the items to be retrieved Notes 1 A fitted model must be present in memory when the command is given or else it has no effect Either an estimation run has previously been performed or a previously stored model has been loaded using the Model Manager Ze When the Retrieve command is given the checks in the Options Output and Retrieval dialog are removed so that the same items are not saved twice 3 Items can be retrieved automatically following a run by checking them in the Options dialog before launching the run Choose from the Once and Always options in this case The former removes the checks after saving 92 James Davidson 2008 6 11 Actions Simulate Current Model This selection generates and displays a stochastic simulation of the current model The user is prompted to choose to discard the series after viewing or write to the data set and in the latter case to either add the series as new variable s or over write the existing dependent variable s Notes 1 To select the mechanism generating the artificial shocks see Options Simulation and Resampling Options The choices are Gaussian model according to likelihood function adopted and a bootstrap of
2. Dynamic Equation dialog is optional though recommended If set it they should correspond to the normalized variable s in the supplied functions These settings are not used to compute the estimates but allow the correct plots series and forecasts to be generated It is the user s responsibility to set the sample period see Setup Set Sample to ensure that all observations are available for the variables in the model This is done automatically for models specified through the program options but the program cannot know whether variables included in the user s function have missing observations For statistics and data generation there is the option to enter names 72 James Davidson 2008 for constants in the parameter name fields then set values for these in the Values Equation dialog These values are not modefied by TSM but are passed through directly to the user s function If this feature is utilised 1t provides a means for quick changes of specification without editing the code To generate data placeholder variables must exist in the data set The contents of these columns is unimportant being replaced by the generated series when the simulation runs For example they can be created using the Extend Sample Make Zero and Rename commands in Setup Data Transformation and Editing Then select these variables as the Dependent Variable s in Model Dynamic Equation 4 5 Model Regime Switching This dialog
3. x Use the File Settings Export command to bundle your data and models into a portable tsm file Create a new directory for each instance and copy the tsm file to each id Start each instance by double clicking on the tsm file see 23 above The directory containing the tsm file becomes the Start up directory for each instance with data graphics tsd model and results files all written there by default For a more permanent multi tasking setup create multiple Windows shortcuts on the Start Menu each edited to point to a different Start In directory Give these shortcuts suitable names to distinguish them Another use for multiple instances is where TSM is running the user s Ox code The supplied Windows shortcut TSM4 with User Code provides an example See Appendix C for further details TROUBLESHOOTING 30 If the program appears to behave unpredictably this may be because a setting has been changed inadvertently For example la The values of certain estimated parameters e g MA parameters GARCH parameters can depend on program settings If a parameter is fixed at zero in the Values dialog no value is reported for it in the output It might appear that the estimated specification is different from the chosen one Note that when variable s are fixed the relevant Values button is highlighted and menu item s checked as a reminder Corruption of the settings file which is reloaded at s
4. 1994 Check the Prewhitening checkbox to prewhiten the data by a VAR 1 regression prior to computing the HAC covariance matrix V V then is recoloured as DVD where D I A 4 1 and A is the VAR coefficient matrix NOTE Use prewhitening with caution It may inappropriate e g in construction of test statistics for I 0 by overcompensating under the alternative The plug in bandwidths are set as the minimum of the value returned by the formula and sample size 2 Larger bandwidths can be set manually MODEL SELECTION CRITERIA 28 A model selection criterion is needed for three automated model selection features Automatic regressor selection see the Actions menu and Setup Automatic Model Selection H Lag selection in the augmented Dickey Fuller test Lag selection in the Stock Watson Saikkonen augmented least squares estimator for cointegrating relations The radio buttons allow a choice of the Akaike Schwarz and Hannan Quinn criteria for these purposes LM TESTS OF RESTRICTIONS AND FIXED VALUES 29 Check the LM Tests of Parameter Restrictions box to compute the score LM statistic for restrictions imposed on the parameters in the Values dialogs There are two modes of operation of this option If parameter constraints have been activated in the Parameter Constraints dialog these restrictions only are tested If parameter constraints are not set but parameters have been fixed in the Values
5. Axis is selected in Graphics Show Data Graphic there may be two zero axes marked for the left and right hand scales respectively SCATTER_PLOT OPTIONS 28 Scatter plots styles allow the form colour and size of symbols to be chosen Scatter 1 is used for all data plots and for actual fitted plots 120 James Davidson 2008 29 30 Scatter 2 is used only for the post sample actual forecast scatter when the one step forecasting option is selected By default scatter plots of data include the two regression lines X on Y and Y on X In the case of the actual fitted scatter the single line with slope 1 is drawn a 45 degree line when the axes match These lines can optionally be suppressed The RGB Scatter option colour codes the plotted points according to their position in the sample The initial points are coloured red those in the middle green and the end of the sample blue with a smooth interpolation from one colour to the next Try plotting the scatter of a variable against the trend dummy to see the effect Select a filled symbol square circle or triangle for best results If monochrome plots are selected the coding is a greyscale running from black to white This option is not available for actual fitted plots which include post sample actual forecast points 8 6 Options ML and Dynamics ML PARAMETERIZATION 1 The residual variance and GARCH intercept are scale dependent parameters bounded b
6. Dynamic Equation or Model Linear Regression Notes l Up to 10 linear restrictions can be specified with nonzero constant terms However up to 20 additional restrictions could be set with zero constant terms 2 Estimation subject to constraints is not available with OLS and IV estimation This option is disabled greyed out when the Model Linear Regression dialog is open 3 By default the statistic reported is asymptotically chi squared Set the check box to report the F statistic with the reported p value taken from the F tabulation Note that this setting is shared with the user specified LM and moment tests see Actions Compute Test Statistics It can be selected deselected in any of the relevant dialogs REGRESSOR SIGNIFICANCE TEST 4 The option Test Joint Significance of Regressors provides a valid time series implementation to the F test of the regression computed by many 75 O James Davidson 2008 9 packages In a single equation it sets up a Wald test of the joint significance of all regressors in the mean model all Types and components of equilibrium relations if any but excluding the intercept trend and seasonal dummies and lagged endogenous variables The null hypothesis can therefore be set up as a univariate time series representation of the dependent variable Note that this test can be performed in the usual way by selecting the parameters individually in the Values dialogs but this
7. Histograms are not displayed for two or more densities in the same graph even if this option is selected The saved plots can be exported to a spreadsheet file for subsequent reloading and or merging with those stored in a different settings file Pressing the Save Plot Data button opens the file dialog for saving Notes Reload plots with the command File Data Load Tabulations Density Plot File The spreadsheet format is as follows Row 1 Plot names Row 2 Kernel bandwidth index integer 0 32 Row 3 Initial bin ordinate Row 4 Increment bin width Rows 5 Histogram values 100 James Davidson 2008 8 Options 8 0 Options General Information and Defaults By default only one Options dialog is open at a time Opening a second dialog causes the first to close This behaviour is optional see General Options The lt lt lt and gt gt gt buttons at the top of each window allow easy navigation between the options dialogs Pressing them opens the next previous options dialog so that current program settings can be reviewed rapidly DEFAULTS The default settings are as follows These are selected if the file settings tsm is not found in the working directory at start up or on the command File Settings New x in the left hand column indicates that this setting is stored with a model and hence is liable be changed when a model is loaded Output and Retrieval Options Save Data to Files of
8. LADA inte eased a na 21 LEMA ORO don a 22 TYPING FORMULAE sev iscdeveceus ide sucbedutvcvts r aa R RE a E ETNE 22 RESERVED NAMES scott ti 24 Pile eas suadits vedvevadessoasacwedeivdacca sostea ecuededasapena na n adeua ii 26 2 0 File General Information rro ita rita qee 26 O A A 27 RESTAR Tati REA eases ee ac De ee ee 27 ZA ERAS a 28 IMPORTING MODELS siii lit berlin 29 EXPORTING SETTINGS secvcsaceces n a lets ot aia tirita iii 29 SETTINGS AS TEA Toronto ha tect e Geass teat cousth E Ein desean A ERR OaE counts 30 2 2 Piles Dat a oa 30 MISSING OBSERVATIONS cccccsesstvesnocssssvonsesbarescnevcsneechoveesievengeesstecenssesnacoessbednesensersens 32 PERIODIC OBSERVATIONS AND DATES eeceeececescesseeceseeeeneeceeeeeneeceeeecsaeceeneeeaeeeses 32 DATED OBSERVATIONS 0 A ce as 33 2 3 File RE e o oe ds 34 DA ASIS A AA 35 2 53 Biles rap id ist Soma haa canes 35 O E e O A E T 36 Sil Setup Set Sample iii anana a iE 36 3 2 Setup Data Transformations and EditiOB oooocnnnccccnncccnoncncnnncnononcnonannncnnnnnnnns 36 EDIT COMMANDS cota 37 TRANSFORM COMMANDS wics cccsccsccssessssssseetessiveeccooucenasedusuvevacscusneesuecobseevsaposecuedsneaesseneeed 40 3 3 Setups Model Mana nrun tesit seo ses ttie a Eei oina 42 STORING MODELS ena aaa ETE E E E AE RE S 43 LOADING MODELS cunas aa 44 DEFAULTS oE A E ATE TE EA ceda 44 MODEL DESCRIPTIONS aa aa E EAR K E RE EEA a 44 DELETING MODELS suas aaa 45 3 4 Setup Automatic Model Selection
9. Monte Carlo graphics can be stored and displayed independently of the DGM that produced them This allows the results of different runs to be proure together for comparison Highlight the plots to be stored as Click on Add to Store A In the text box that opens the current name is displayed Edit or replace this name to identify the plot in a comparison of DGMs Click OK or press the Return key to close the text box ES Repeat the naming procedure for each plot selected 99 O James Davidson 2008 Note The stored plots are saved in the settings file not in the TSD file associated with a model To display the stored plots select Graphics Stored MC Distributions from the menu id Select and display plots as usual Highlight a name and click Rename to re open the text box and type a new name Note Only one plot at a time can be renamed A Highlight any number of names and click Remove to remove the graphics from the store Highlight one name and click Move Up or Move Dn to change the order in which plots are displayed Note The bandwidths for stored plots can be changed in the same way as described in 3 To show two or more density plots in the same graph for comparison select the Options Graphics from the menu and then One Graph in Multiple Series Display The MoveUp Dn buttons allow control over the colours or line types used to display each plot also the order in which legends appear Note
10. Nonlinear MA With this option the model disturbance term Ut is replaced by the moving average formulation Ut Et f3 Et j j gt 0 Enter the formula for the function f3 using the reserved variable names E j to represent the disturbances lagged j periods E here corresponds to v in equation 3 29 of the main document As in Residual the formula should be in implicit form do not include In multi equation models use the variable names E 1 j E 2 j to represent the disturbances for each equation Presample lags are replaced by 0 Notes 1 With this option the function has to be evaluated recursively Iterative estimation of these models could be time consuming 2 A pre programmed nonlinear MA model can be accessed from the Model Dynamic Equation dialog and should be faster to estimate than the coded version Use this option except to implement other variants If both options are selected the coded version takes priority Nonlinear ECM Notes In error correction models equations can contain nonlinear functions f2 Z of the lagged equilibrium relation Z Three popular forms are pre programmed For other cases enter the function s f3 in implicit form using the reserved variable name Z to denote the equilibrium relation or in case of two or more relations the names Z 1 Z 2 Lags can be included as Z j for j gt 0 Note that the lag j is relative to the minimum lag specified in t
11. Run is displayed in the text box where denotes the current run ID number The entry can then be edited as desired If an existing title is first highlighted this name appears in the text box If OK is pressed without changing it the current specifications overwrite the ones stored under that title This option allows a stored model to be modified or updated Rename a model by loading it saving it under the new title and then deleting the original copy The Store command places the model specifications in a memory buffer but does not save them to disk Give the command File Settings Save or Save As to save them permanently in a tsm file When a settings file is reloaded the stored models it contains will be accessible as before The least squares and IV estimation options have different actions depending on whether estimation is launched from the Linear Regression dialog or the Dynamic Equation dialog In the latter case estimation is done numerically To make sure the desired estimator is recorded as part of the stored model have the appropriate dialog open when the Store command is given There is an option to store the estimated model automatically following a successful estimation run see Options General Note that a maximum of 50 models can be stored To store additional models save the settings in a named tsm file see File Save As In addition to parameter values results and listings associated wi
12. The program automatically saves all current settings in a special file called settings tsm When the program is restarted the working environment with all selected options is exactly as it was in the last session There is an option to discard model specs at shut down and save only the current options Named settings files with tsm extension and red TSM Windows icon can be saved and re loaded manually at any time 5 ORGANIZING YOUR WORK The File Settings Export command saves a complete image of the current session including options model specifications data generated series tables and graphics Exported tsm files do not contain local path information and are fully portable between installations When they are opened the data file and temporary storage tsd files are recreated This provides an ideal way to share work with collaborators move between home office installations and distribute classroom exercises Double clicking on a tsm file icon in Windows Explorer starts the program and loads the file contents automatically 6 SIMULATION Part of the TSM philosophy is that any model that can be estimated by the program can also be simulated using randomly generated disturbances or bootstrapped randomly resampled residuals The former can be Gaussian or generated from the distribution specified by the selected likelihood function This feature can be used for one off simulations whose output is graphed Compari
13. associated Q statistics using the scroll bar If this is set to 0 no correlograms are computed Choice of Box Pierce or Ljung Box Q test variants is selected in Options Tests and Diagnostics 4 Check the Data Correlations box to see the correlation matrix of two or more series In this case no other statistics appear and the correlograms scrollbar is greyed out If only one series is selected with this option set no output is produced S Check the Quantiles checkbox to report the following quantiles of the data distribution 0 01 0 05 0 1 0 3 0 5 0 07 0 09 0 95 0 99 For small samples the extreme cases are omitted Note that if detrending is specified the mean of the distribution is zero by construction 47 James Davidson 2008 6 The Sample button opens a dialog to set the sample period to be analysed Sample 2 See Setup Set Sample for details de The test p values are computed from the published tables and are not available for every ordinate The values given are upper bounds Dickey Fuller s table for the maximum sample size is quoted for the ADF and Phillips Perron tests and in this case the probabilities refer to the lower tail 3 7 Setup Nonparametric Regression Opens a dialog to specify a Nadaraya Watson estimate of the conditional mean using the Gaussian kernel Two variables must be selected from the list the dependent variable y and regressor x Use the radio buttons to toggle between
14. Bootstrap selected in the Options Simulation and Resampling dialog Set the shock variance in the same dialog for the Gaussian option and appropriate parameter values in the Values dialogs for the Model option Make these selections before saving the DGM 51 James Davidson 2008 Between 1 and 1 million replications can be specified The selectable values are in the ranges 1 2 5 10 50 100 1000 1500 10000 15000 100000 150000 1000000 If a test takes a variable parameter such as degrees of freedom or number of tested restrictions the tables display this value enclosed in square brackets appended to the test name The suffix is omitted if the parameter has a default value such as 1 in the case of t ratios OPTIONS 8 10 11 12 13 14 The parameter moments reported are the mean standard deviation skewness and kurtosis of the Monte Carlo distribution of parameter estimates Optionally moments can be computed for the estimated standard errors of the estimates using whatever formula is specified in the estimation model standard robust or HAC The mean of this distribution may for example be compared with the SD of the Monte Carlo distribution of the estimate Parameter biases and RMSE can be reported in cases where the DGM and the estimated model have comparable specifications If the models are not comparable having different sets of parameter names this option is cancelled a
15. Davidson 2008 the dialog is refreshed or the Values button pressed in the relevant dialog 6 If a dialog gets hidden behind others bring it to the top by reselecting it from the menu bar 7 Default settings set with New in File Settings are listed in Option General 1 2 Status Bar and Tool Bar The status bar at the bottom of the results window shows the name and path of the currently open data file the currently selected estimator and the currently selected sample The symbol B also appears if bootstrap inference is selected and the symbol S if subsampling inference is selected The tool bar buttons provide quick access to the most frequently used actions and dialogs s Open Folder button shows the File Data Open dialog f x button opens the Setup Data Transformation and Editing dialog 5 MM button opens the Setup Model Manager dialog Regression line button opens the Model Linear Regression dialog a Space Shuttle button optional opens the Model Dynamic Equation dialog E Running Man button optional normally launches Actions Run Estimation Also duplicates the function of the Go button in an open dialog Calculator button launches Actions Evaluate at Current Values This is equivalent to Actions Run Estimation in the case of linear regression a Chart button Dual action o Displays the plot of the variable s selected in the variable list in any di
16. E aria ian ke EE E EEE EE ie 75 CODED RESTRICTION Sei rr a E a rR is 76 4 7 Model Equilibrium Relations ii it a ias T11 4 8 Model Select Instruments inicial iia 79 Ve des a dde tio De e R 81 5 0 Values o 81 BUTTONS EE E E E E E TE 81 VALUES FIELDS sit a AAA ede E E 81 FIXED PARAMETERS 0 3 csc secchscresses cocndecs sedated desatar A ER E E E n E Eee SEEDER cones 81 PARAMETER BOUNDS 3 oc cosedvctesies cc cndees dico dal atan idad coos 82 GRID PLOTS cidcid ee E E E adela 82 WALD TESTS AND LINEAR RESTRICTIONS c ccccococononoconononononononnonononnonnnonnncconnnnncnnnnnnno 82 5 1 Values Equation viii salen 83 5 2 Values Equilibrium Relato Semi iio 84 5 3 Values DISTAL TR 84 5 4 Values Switching Regimes as 84 ACETO OS 86 6 1 Actions Run Estimation sseesseesseesseesseeeesseesseessersseesseresseeesseesseesseesseeessees 86 BATCH JOBS 00 a E tin 86 6 2 Actions Evaluate at Current Vales iia 86 6 3 Actions Estimate Multiple ARMA Models oooooccconcccnonoccnononccoonccononccinnncnons 86 6 4 Actions Automatic Regressor Selection oooooonocccnoncccnoncncnoncncnnncnonnncconnnncnnns 87 6 5 Actions Recursive Rolling Estimation ooooccononcccnnocccnonancnnonanonancnnonnccnnnncnnns 88 6 6 Actions Plot Criterion Ad a 89 6 7 Actions Multi Stage GMM La 89 6 8 Actions Compute Test Statistic ont ido init 90 SCORE LM TES e a tes a a e E 90 MOMENT M or OM IES a a a E a abies A e E 91 WALD TEST OF SET RESTRICTIONS
17. Options General Options OPERATIONAL SETTINGS 1 Dialogs are closed when an estimation run is started Checking the option Restore Dialogs Automatically causes them to re open in the same positions at the end of the run Dialog positions are stored in settings tsm so the last configuration in the previous session will also be restored at start up If this option is not selected dialogs can be restored manually using the Actions Restore Dialogs command The positions of dialogs on the screen are remembered during a session but by default are lost when the program is closed They are positioned centrally when first opened Optionally the program will remember the positions 125 James Davidson 2008 between sessions This allows the user to maintain a preferred screen layout but note that 1f the monitor resolution is changed they could become invisible In this event use the command Actions Reset Dialog Positions to re centre them By default the user is prompted to save data results before over writing them or closing the program Deselecting Enable Saving Prompts suppresses these reminders Saving program settings in a file allows the exact state of the program to be restored by reloading the settings These include the data file sample model specifications and current estimates This can always be done manually but the option Save Settings After a Run saves the settings automatically in a file run ts
18. Sample dialog for selecting the sample A data file created with GiveWin will contain the date information If using Excel or other program to create the data file the date information can be included in the following way Create a variable with the name ISTARTDATE This must have entries in the first three positions as follows l The year of the first observation 32 James Davidson 2008 10 11 Ze The period quarter month week weekday day of the first observation 3 The frequency one of 2 half years 4 quarters 12 months 52 weeks 260 weekdays 365 days The rest of the column can contain anything or be blank This item is removed after being read so it will not appear in the variable list If you now save the data file it will contain the date information in Ox format the first column of the file will contain the dates in the format year period This column will be used to create date information next time the file is loaded If files are merged the date information of the first loaded file is used unless the merged file contains a STARTDATE column in which case this information is used to date the combined observations However GiveWin date information in the merged file is ignored The periods must have equal length e g no missing holidays or leap years in daily data Otherwise the data must be treated as undated However ignoring these irregularities may be permissible for labelling
19. against attempting to append text to an existing binary file results files must have extension txt This is appended to the chosen name if it is not present 5 Yet another way to save results is to use the Windows clipboard Just highlight the desired text in the results window Copy right click for the context menu and Paste into your favourite text editor 6 The Locate Results Folder File command displays a text field containing the current path to the results folder This can be edited to change the folder If the new path does not point to an existing folder the change is ignored NOTE if no path is displayed this means that the results folder is the same as the Start in folder the default 34 James Davidson 2008 Pressing the Locate Results File button displays both the path and the name of the current results file The text can be edited to set a new results file and or path This is an alternative to giving the new Results File command to open the file dialog Either method of changing the results file also changes the results folder to the one containing the file Graphics are always saved in the current results folder The Start in folder is used as the results folder by default but note that the current path is saved between sessions in settings tsm 2 4 File Listings This command saves different types of estimation outputs in tabular form Series Actuals Fitted Values Residuals Cond
20. and Smooth Transition models the dialog shows the parameters of these switching models Notes 1 In the Markov case the switching probabilities are constrained to be positive with their sum in 0 1 such that the implicitly defined Mth probabilities are nonnegative These are transformed to unconstrained values t_ ji for 84 James Davidson 2008 estimation using a logistic map See the main document for the mapping formulae These values are displayed in the output with standard errors To show the t_ ji values in the dialog with upper and lower bounds transformed similarly when shown check the Display Logistic Transformations checkbox By selecting the Estimate Regime Differences option the Markov switching probabilities can for example be constrained not to depend on the current state Under this hypothesis the sample is simply a random mixture of regimes prevailing with the unconditional switch probabilities Note that the null values of the incremental probabilities of regimes 2 M are 1 M corresponding to t_ 32 t_ jM 0 If regime dependent coefficients are specified in Explained Switching use the Next Regime button to cycle through the regimes or the Regime choice widget on the toolbar to select a regime directly Note that specifying only the intercept and regime dummies in the explained switching model provides another way to estimate the simple Markov switching model in an alternativ
21. appropriate in the redesigned Linear Regression and Dynamic Equation dialogs A Parameter Bounds Grid Plotting checkbox is located in each Values dialog The Minimand option is selectable in Options Optimization and Run Kernel selection for HAC estimators has been moved from Options General to a redesigned Options Tests and Diagnostics dialog a The Options Bootstrap and Simulation dialog is now renamed as Simulation and Resampling and controls both bootstrap and the new subsampling options The new Dialog toolbar button can be used in two ways By default it re opens the last dialog closed excepting dialogs with their own buttons Hover the mouse over it to see its current assignment Alternatively it can be permanently assigned to one of a range of dialogs normally accessible from the menus Set your choice in Options General 8 James Davidson 2008 0 Introduction 0 1 TSM Basics TIME SERIES MODELLING Version 4 is an interactive package for modelling and forecasting time series It is designed primarily for nonlinear dynamic model estimation including ARMA and ARFIMA models conditional variance models ARCH GARCH and several variants regime switching and smooth transition It also functions well as a user friendly general purpose regression package To enhance its power and ease of use the program has various special features not found in comparable packages It is strongly recommended to read thro
22. buttons on the tool bar Notes 1 Open the Set Sample dialog using the Sample button to set the desired sample Sample 4 This selection is independent of those set for other program functions See Setup Set Sample for details The KPSS test of I 0 and P P test of I 1 are also available in the Actions Summary Statistics dialog but here for convenience are computed for all the selected variables at once The p value inequalities reported are taken from the tables of the eigenvalue and trace tests in Osterwald Lenum 1992 A check box allows the inclusion exclusion of drift terms in the CIVAR If the drift is suppressed intercepts of the estimated cointegrating vectors can be computed However note that standard errors are not computed for these MINIMAL analysis is described in Davidson 1998a A sequence of chi squared tests is computed to estimate the set of irreducible cointegrating relations such that cointegration is not a property of any subset of the included variables Identified structural cointegrating relations must belong to this set If the cointegration hypothesis is not rejected estimates of the vectors are reported with asymptotically valid standard errors and Phillips Perron statistics for the corresponding cointegrating residuals There is the option to specify a single test of the hypothesis that the cointegrating space contains an element subject to specified zero restrictions When
23. device aimed at reducing the error in rejection probability of bootstrap tests It is not guaranteed to improve performance in all cases but showing that test outcomes are invariant to this selection offers additional robustness RESAMPLING CONFIDENCE INTERVALS 19 Resampling allows true confidence intervals for parameters to be estimated Three schemes for 95 confidence intervals are implemented Equal tails 2 5 of probability mass in each tail but if the distribution is skewed the point estimate is not the mid point of the interval Equal tails percentile t intervals based on quantiles of the distribution of t statistics weighted by standard errors from the resampling distribution Symmetric percentile t intervals based on 95 quantile of the absolute t statistics centred on the point estimates but tail probabilities are unequal if the distribution is skewed NEWTON RAPHSON ALGORITHM 20 21 22 The model is re estimated with simulated data in each replication For models estimated through the Dynamic Equation dialog this means numerical optimization Since the true values defining the artificial DGP are available for starting values the Newton Raphson algorithm is used for these steps The numerical Hessian of the criterion is evaluated at the true point Numerically precise convergence is not required to reproduce the distribution adequately The time taken in the replications can be controlled by
24. dialog and in the panel Print in Results Window check the option Forecasts amp MA Coeffs If the model has already been estimated click the Calculator button on the tool bar This will evaluate the model and forecasts Otherwise click Running Man to run the estimation and forecast calculation in one step To see the point forecasts and confidence intervals graphically select Graphics Ex Ante Forecasts The forecasts can also be exported to a spreadsheet file Click File Listings Save Forecasts 10 HOW TO ESTIMATE A SIMPLE VAR MODEL x Open the Linear Regression dialog and check the box System of Equations You are now allowed to select two or more dependent variables In the Select Regressors panel click on the Type 2 radio button Make the same selections as you made for the dependent variables Use the Lags scroll bar to choose the VAR order Select an intercept if desired Any exogenous variables can be added to the model as regressors of Type 1 Press Go or the Running Man or Calculator buttons to estimate the model Note that when endogenous variables are entered as Type 2 Regressors the current values are automatically suppressed making it easy to specify lagged dependent variables A VAR or VARMA can also be estimated in the Dynamic Equation dialog 16 James Davidson 2008 11 HOW TO ESTIMATE A GARCH MODEL Open the Dynamic Equations dialog i Specify the mean equation as appropria
25. file is used as the Start in directory If it contains a settings tsm file the settings are loaded from there Otherwise the defaults are set and a new settings tsm is created 140 James Davidson 2008 RUNNING SEVERAL INSTANCES OF TSM 25 26 2T 28 29 To run lengthy optimizations or Monte Carlo runs without tying up the program interface try the option for exporting batch jobs to be run from the command line For details see BATCH JOBS under 6 1 Actions Run Estimation and RUNNING AN EXTERNAL PROCESS under 3 10 Setup Monte Carlo Experiments When these jobs terminate their outputs are written to text files with the run number Give the command File Load Text File to write the contents to the results window in the usual way By default a batch job is launched automatically to run concurrently with the GUI This is the efficient way to make use of a dual core processor since TSM is not multi threaded even under Ox 5 Alternatively the run or runs can be postponed to a time when the machine is otherwise idle In this case they must be launched manually as regular Ox programs It is also possible to run two or more instances of the GUI concurrently The only major problem to be avoided in this case is the different sessions interfering with each other by attempting to access and write to the same files The trick is to create a different working directory for each instance In Windows do as follows
26. from the experiment last run with the currently loaded model Multiple experiments can be set up by selecting two or more models in either category O If one EM is selected and two or more DGMs then the experiment is performed on the EM using each DGM in turn o If two or more EMs are selected and one DGM then the experiment is performed on each EM using the specified DGM o If multiple models are selected in both categories then all the possible experiments are performed each DGM with each EM in turn o The same model s can be selected in both categories In a single experiment pressing Run a second or further time results in additional replications the number currently selected being added to the current set To start a new experiment change any model selection or any option other than number of replications This feature is not available when multiple experiments are specified The sample period for estimation is always defined by the DGM The sample settings for the EM are ignored To have a dynamic simulation run for a number of start up periods select the Presample Data Random in Simulations option in Options Simulation and Resampling Then set the DGM sample period as desired for estimation If no models are defined the current specifications are stored as a model with the default name run ID and used for both DGM and EM The DGM specification MUST include a choice of shock distribution Gaussian Model or
27. from the following components depending on the formula type as indicated AC variables by name or number see Notes 1 5 optionally followed by an integer lag negative value or lead positive value enclosed in braces BC parameters by name or number see Notes 1 6 ABC real numeric constants containing digits 0 9 optionally including a decimal point and optionally preceded by a minus sign ABC the operators add subtract multiply divide raise to a power ABC parentheses enclosing sub formulae ABC the functions log exp cos sin abs sqrt int sgn pos and neg where the parentheses can contain a variable parameter constant or sub formula ABC The names Pi pi PI and pl are reserved and are replaced by the constant 3 14159 to machine accuracy Notes l The first character of a variable or parameter name MUST be a letter from the sets a z A Z 2 The following characters can also appear in variable or parameter names amp 0123456789 lt gt _ l 3 Names are case sensitive E g Alpha ALPHA and alpha are all treated as different names 4 An alternative to typing a variable name in full is to type x i or X i where i denotes the number of the variable in the data list When the text field is opened variable numbers are appended in the appropriate data list i e x In case A Setup Data Transformat
28. i where i is the parameter number shown beside the text field is always a legitimate choice of name It must be still typed explicitly in the 70 O James Davidson 2008 field so that the program knows how many parameters are specified Nine parameter name fields are displayed by default To change the number type the value in the Maximum Parameters field To redraw the dialog box click any button e g Cancel Be careful that parameter names do not duplicate variable names The convention of naming a coefficient by the variable it multiplies must be avoided here ll In multi equation models the same names appear in each equation but refer to different parameters They are distinguished in the output by prefixes Eql Eq2 etc If a parameter is named but does not appear in an equation it is fixed at 0 in that equation It appears in the Values dialog but is suppressed in the output This allows equation specific parameters to be named distinctively VARIABLE NAMES These can be spelled out in full or replaced by the short form x i where i is the position of the variable in the list starting from O The line numbers are displayed in the variable list in Models Dynamic Equation whenever the text field is open Under the Equation coding option select the the dependent variable s in the Model Dynamic Equation dialog first Unless the formula fields already contain formulae press Clear to delete the
29. in a include compiler directive in usercode ox In this case K any executable code in usercode ox itself is ignored only the first include directive in usercode ox is recognised Any additional inclusions are ignored T Any text in the results window which is highlighted when the File Export command is given is stored in the settings file and written back to the results window at start up This trick allows instructions and notes about the contents of the exported file to be easily conveyed to recipients of the file 29 James Davidson 2008 SETTINGS AS TEXT 8 10 The Display Save Settings command opens a choice box with the options of printing the text in the results window and opening the file dialog for saving the text In the latter case a txt file extension is recommended See the programming manual for details of the scripting language The Save Current Model command saves just the loaded model settings to a file To view these settings in TSM store the model with the Automatic Descriptions option checked then click the Model Description button The main function of this command is to allow the settings to be imported into another instance of TSM using File Restart Load Text Input The Save System Defaults command saves a file for loading at start up This options allows the user to control the state of the program set by the File Settings Clear All command or renewing the
30. maximum can be reset to any desired value in the text box 121 James Davidson 2008 There is no accepted convention regarding the signs of the coefficients of a moving average lag polynomial The program default is to report the MA coefficients theta_ in theta L 1 theta_1 L theta_q L q and GARCH coefficients as beta_ in beta L 1 beta_1 L beta_r L r This 1s consistent with the convention in equation 4 of the main document and also more natural For example in the ARMA 1 1 model equal roots cancel each other out and in this case the estimates will be equal Similarly in the ARMA in squares representation of the GARCH 1 1 model beta_1 delta_1 corresponds to alpha_1 0 and the estimates are again equal in this case However the MA coefficients can be optionally reported as theta_j in theta L 1 theta_1 L theta_q L q and GARCH coefficients as beta_j in beta L 1 beta_1 L beta_r L r If the first observation for estimation is greater than 1 lag distributions will normally be computed using all available pre sample lags Checking Restrict Pre Sample Lags allows the number of presample lags to be set in the textbox provided Thus setting Lag Truncation to O means that all pre sample values are replaced by 0 This provides comparability with the situation when the first observation used for estimation is 1 For details of the option Type I Fractional see 4 2 Model
31. may be estimated subject to the caveat of containing only one endogenous variable each but may NOT be used for simulation It is the user s responsibility to respect these restrictions The program cannot monitor violations and incorrect estimates and simulations will result De When the Coded Equilibrium Relations option is selected in the Model Equilibrium Relations dialog only the Residuals option is selectable in this dialog TEXT BOX CONTROLS Cancel Discard changes and restore existing formula Clear Clears displayed formula Enters left hand side for Equation entry Next Displays the next formula where present disabled otherwise Previous Displays previous formula where present disabled otherwise Test Tests parsing of the current model equation s Closing the dialog with the Windows Close button x is equivalent to pressing Cancel PARSING THE MODEL Parsing fails in cases including the following ll Variable name does not match any variable in the data set x Non matching or misplaced brackets parentheses braces F Missing misplaced operators Wrong left hand side variable Equation An error message is displayed in a pop up window and should assist the debugging process Note A name not appearing in either the variable list or current parameter list is assumed to be a new parameter and added to the list Check the list carefully to see if it s what you intend PARAMETER NAMES P
32. of the explained switching model In the first 73 James Davidson 2008 10 11 12 13 14 15 16 version the equation for the probability of switching into regime j at date t may depend on the current regime 1 only through an intercept shift by inclusion of a dummy variable for the intercept in question with Regime 1 as the reference case In the second version the switching equations may be fully regime dependent and switch just like other model components Check the box Regime Dependent Coeffs to enable this case The second explained switching model contains the first one as a special case but the latter is set up in a slightly different way with regime dummies and is retained for backwards compatibility and simplicity If dummies or switching intercepts but no explanatory variables are specified in explained switching the model represents an alternative parameterization of the regular Markov switching model In form log odds transformations of the switching probabilities are estimated as unconstrained parameters and standard errors and test statistics are implemented In the smooth transition ST case select the transition indicator z_t from the variable list after clicking the first radio button Only one selection is possible If no transition indicator is selected the smooth transition option is cancelled and the type setting reverts to Markov switching The inclusion of an ST intercept is
33. on the tool bar All have the same action in this case t The results appear in the window To view the Actual Fitted and Residual plots click the Twin Graph button on the tool bar To use less than the complete sample for estimation click the Select Sample button to open the sample setting dialog Use the scroll bars to 14 James Davidson 2008 select the first and last observation When you launch an estimation run open dialogs are closed automatically to show the results window Click the Windows button on the tool bar to restore them to their previous locations on the screen 4 HOW TO GENERATE QUARTERLY DUMMIES Click the f X button on the tool bar Click the Edit button then scroll down the choice widget until you find Make Seasonals A scroll bar to choose the frequency appears Select 4 and press Go Four dummy variables are added to the data set Add only three of them to your regression if you have an intercept 5 HOW TO TAKE LOGARITHMS OF YOUR DATA Click the f X button on the tool bar Click the Transform button then scroll down the choice widget until you find Logarithm Highlight all the variables on the list you wish to transform Click Go The transformed variables are added to the data set identified with the prefix Log added to the name To give a more convenient name if desired select Edit and Rename with the choice widget and enter the new name in the field provided 6 H
34. ooonccnnnncccononacononanononacononacononononnnanoons 45 AUTOMATIC REGRESSOR SELECTION c cc ceecesseecsseeseeceseceeaeeceeeeeneecseeeeneeceseeeeneeeeee 45 MULTIPLE ARMA MODELS isis taa cod vaneominbhs E AAN 45 3 5 Setup Recursive Rolling Estimation ccceeseecesseceseececseeeeceeeeeeseeeeenaeeees 46 3 6 Setup Compute Summary StatiStiCS ooooocnnncccnoncccnoncccnnonnnononanonanccnnnnncnnnnnnnns 47 3 7 Setup Nonparametric Regression vincia cidcid seins 47 3 8 Setup Semiparametric Long MeMory eeecccceseceeeeeceeeeeeeceeeeessteeeenaeeees 48 3 9 Setup Cointegration Analysis A 49 3 10 Setup Monte Carlo Experiments cccssssccssssescsesssesssscssssscesnsncecensecscnsacess 50 A O ONO 52 RUNNING AN EXTERNAL PROCESS 00 cee eeecceeeesnceceseeesnceceseeeeneeceseeeeacecenesenaeceeeeeeneeenee 54 ADDITIONATE OPTION S nren unna didas didas E ds subse thcuedus de tunscste cule de cdo elas des 54 3 11 Setup Tail Probabilities and Critical Walues ooonoonnnnnnonccnnconnccnoncconccnnnos 55 Model A 56 4 0 Model General cies et aedni tae auld saber 56 BUTTONS ciaie Sa aaas e a ea ea nets Seine E E ts 56 SPECIFYING SYSTEMS OF EQUATIONS cccceesccescsessseceeeeecaeceeneecsaeceeeeecaeceeeeesaeeesees 56 4 1 Model Linear RES reSSi OM narrando id 57 VARIABLE AND LAG SPECIFICATION ocooocccocccconnnonnncnnnnnnnncconnnnnnnccnnnnnnnnccnnnnnnanccnnenrnnnccnnes 59 WALD TEST OF CONSTRAINTS eoa e aE EEA E ERR erro 59 CO
35. reduce M p 1 series down to M For the explained switching model the M 1 series of variable switching probabilities are also plotted When regime dummies have been specified there are up to M 1 different series for each regime although differing only by the same offset at each t These are averaged to create the series 132 James Davidson 2008 21 plotted For the smooth transition model the regime weights are plotted logistic functions of the transition indicator BOOTSTRAP AND SUBSAMPLING P VALUES 22 23 24 Resampling computing p values for tests by tabulating the statistics for a pseudo true model where the statistics are centred using the relevant components from the sample counterparts This method can be used for t ratios and Wald tests and also M and CM tests It is not so easily implemented for LM tests although diagnostic tests for i i d residuals are valid by construction in the bootstrap context Other LM tests and other tests are given their conventional asymptotic p values Note that resampling p values are always indicated with a Resampling p values are computed for the Jarque Bera test only for the bootstrap using Gaussian shocks Otherwise the hypothesis is true by construction so the bootstrap p values are uninformative The cointegration tests ADF and Phillips Perron cannot be resampled since there is no way to set up a pseudo true version of the null hypothesis Note that in singl
36. rescaling the default set the factor to 0 SIMULATED ANNEALING 7 Optionally a simulated annealing algorithm can be run for a fixed number of iterations to provide starting values for BFGS This option is selected by default By choosing a large number of iterations SA can be effectively made to act as the search algorithm proper However given good starting values BFGS should be much faster so a compromise is probably best The other three settable SA parameters are the initial temperature the temperature reduction factor and the number of iterations before temperature reduction None of the defaults are necessarily best If the number of iterations before temperature reduction is set lt 1 it is replaced by the default of max 100 5 parameters This setting appears as NaN in the text field NON CON VERGENCE 9 If the BFGS search algorithm reports convergence failure then by default the parameters are set to default values and no output is returned Optionally however the output can be printed as usual using the current 124 James Davidson 2008 point attained by BFGS Be cautious in interpreting these values and especially standard errors A possible cause of failure is a non unique likelihood optimum In that case the reported values should represent an optimum point but the standard errors and covariance matrix are typically not meaningful RUNNING AN EXTERNAL PROCESS 10 11 12 13 14
37. settings file Use the File Restart command to set up the system to read the designated file 2 2 File Data Data can be read in one of seven formats and saved in one of five formats The format is specified by the file extension xls Excel Worksheet The first row of the sheet must contain variable names esv Comma delimited text file Format as for xls wkl wks Lotus 123 worksheet The first row of the sheet must contain variable names in7 GiveWin file See Ox and Givewin documentation for details dht GAUSS data file Not available for saving dta STATA Versions 4 6 data file Not available for saving dat Ox Givewin data with load information file See the documentation for details mat or any other ASCII file containing a matrix with variables in columns and observations in rows The first line of the file must contain two integers number of rows followed by number of columns In this case the variable names assigned are Varl Var2 etc These can be changed in the Data Transformation and Editing dialog The available commands are Recent Submenu to select one of the five most recently selected files Open Any data currently in memory are over written e Opens the operating system s file dialog for opening Any data 30 O James Davidson 2008 currently in memory are over written Merge Merges new file with data already loaded After selecting the file a dialog is pres
38. slow for large systems If the BEKK option is selected the GARCH_M variables consist of the conditional variances and covariances of all equations The SD mode is not available in this case In a system of equations with multivariate FIGARCH or HYGARCH disturbances it is possible to parameterize the fractional difference parameters for Equations 2 as the differences from the parameter of Equation 1 This makes it easy to constrain and test equality of the parameters across equations To select this option which will also apply to VARFIMA parameters if specified set the checkbox in the Model Equilibrium Relations dialog This works even if error correction terms are not specified 4 4 Model Coded Function This dialog is used to set up nonlinear functions coded by the user Coded functions can form complete models for estimation or components of models Test statistics can also be coded See the main TSM document Section 3 2 8 for the details The dialog is also used to specify coded functions for simulated data generation x Specifications created in this dialog are ignored unless the Coded Function checkbox in Model Dynamic Equation is checked The checkbox cannot be checked unless a specification exists The Clear button clears all text fields both the parameter names and the contents of the formula fields Use with caution The Clear Built In Components button is provided as a convenience for the case w
39. the radio button for this option is selected the variable list shows only the currently selected CIVAR variables Select a subset of these to test the hypothesis that they form a cointegrating subset Scroll bars allow the setting of lag length and also the cointegrating rank to be assumed for computing the beta matrix of cointegrating vectors This setting is taken as given in the MINIMAL analysis See Davidson 1998a for details of the rule of thumb adjustment to the chi squared critical values 3 10 Setup Monte Carlo Experiments This dialog provides the options to set up and run one or more simulation experiments To make use of it there should normally be at least one model 50 James Davidson 2008 stored stored using the Setup Model Manager dialog If two different models are one can be used to generate the artificial data and the other to specify the estimation allowing a flexible approach to misspecification analysis x Notes Select one or more Data Generation Models DGM s from the list Select one or more Models for Estimation EMs from the list can be the same as or different from the DGMs Use the scroll bar to select the number of replications and set other options with the checkboxes Press Run to perform the experiment s To interrupt a run in progress press the Stop button on the toolbar with the options of aborting or continuing Press Results to re display the tables
40. these choices Press Sample to open the Set Sample dialog and select the sample to be analysed Sample 3 This sample is shared with the semiparametric long memory estimators and can be set in either dialog By default the bandwidth used is S n 1 5 where n sample size and S is the sample standard deviation of the regressor Use the scroll bar to increase or decrease this setting by factors of 2 The function is plotted with the y x scatter optionally superimposed 3 8 Setup Semiparametric Long Memory This dialog computes estimates of the long range dependence parameter d using one of three semiparametric methods l Narrow band log periodogram regression Geweke and Porter Hudak 1983 The log periodogram points for j 1 M are regressed on 2log sin pi j T where T is sample size and M T gt 0 Broad band log periodogram regression Moulines and Soulier 1999 The log periodogram points for j 1 T 2 are regressed on 2log sin pi j T and P Fourier terms cosine functions of pi j T to approximate omitted short range components where P gt infinity but P T gt 0 Local Whittle Gaussian maximum likelihood Kunsch 1987 Robinson 1995 Maximizes the frequency domain Gaussian likelihood as function of d using the first M periodogram points where M T gt 0 The outputs from this option includes point estimate asymptotic standard error and t test of significance The log periodogram regre
41. values at zero Temporarily restricting a model without changing the specifications Computing LM tests of the corresponding restriction s see 81 O James Davidson 2008 Options Test and Diagnostics Options Evaluating the optimized likelihood over a grid of points see paras 13 14 below and also Actions Plot Criterion Grid for more details If the model specification is changed values are reset to defaults To remove a variable or lag from the model temporarily fix its parameter at zero This preserves other stored values As a reminder that one or more parameters are fixed the Values buttons in the corresponding dialogs are highlighted and check marks appear against the Values menu items PARAMETER BOUNDS 10 11 12 To constrain a parameter to lie in an interval enter the upper and lower bounds in Values but do not check the Fixed box The reported parameter is then a logistic transformation of an underlying unconstrained value The bounds are ignored unless the upper strictly exceeds the lower Cancel the setting by putting both bounds to 0 Tf the estimate is in the interior of the interval the standard error is approximated using the delta method However if the constraint binds in the sample the covariance matrix may be near singular and standard errors unavailable or unreliable It may be best to re estimate with the parameter fixed at its boundary value in this case It is not recommended
42. which additional model features will be activated Use the radio buttons to select an estimator The estimation criteria see main documentation for details are Least Squares Least Generalized Variance FIML Instrumental Variables GMM Conditional Maximum Likelihood with Gaussian normal errors Conditional Maximum Likelihood with Student s t errors Conditional Maximum Likelihood with skewed Student s t errors Conditional Maximum Likelihood with General Error Distribution Whittle frequency domain ML with Gaussian errors Probit 0 1 binary data Logit 0 1 binary data Poisson count data Negative Binomial I count data Negative Binomial II count data 00000000000 Use the scroll bars to choose the order of ARMA model Use the checkboxes to select the ARFIMA long memory specification impose a unit root select a nonlinear moving average see 16 below and include intercepts of Type 1 or 2 and a trend dummy Only one type of intercept can be selected at a time 60 James Davidson 2008 Use the radio buttons to switch between selection of the four categories of variable the dependent variable and regressors of Types 1 2 and 3 Then highlight the variables required in the list l Set the Lags scrollbar to a positive value to include lags up to this order of all the variables of the Type whose radio button is currently selected Use the lower scrollbar to select the number of lags of the err
43. whose size is linked to screen resolution As many graphs as desired can be open at once Close them by clicking the Close button in the top right hand corner or from the Windows taskbar x Clicking on the gnuplot icon in the top left corner of the window opens a context menu Choose Options to open a submenu of useful commands These include changing the text font line style and background colour sending to a printer and copying the graph to the Windows clipboard so that the image can be pasted into your favorite graphics program For bitmaps IrfanView is a highly recommended freeware package which can convert an imported image to a variety of bitmap formats such as jpg Note that the gnuplot window can be resized by dragging the corner with the mouse and a saved bitmap image will have the same dimensions Alternatively pasting the clipboard into a graphics program such as CorelDraw results in a vector graphics image that can be edited further and saved in various formats An alternative procedure to save a graph is with the command File Graphics Save Last Graphic The type of file saved and bitmap dimensions can be selected in the Options Graphics dialog Note that line styles and fonts cannot be selected within the program in this case However the Postscript vector graphics formats eps or epc can be imported into graphics programs such as CorelDraw for further editing 7 1 Graphics Show Data Graphic Open
44. 15 If the option Run Next Estimation as External Process is checked before launching an estimation run the calculations are run in a new instance of Ox running in a console window A temporary executable Ox file is created to be run in batch mode This option allows the TSM GUI to remain under the user s control for other tasks while a long numerical optimization is performed It also allows two or more jobs to run be concurrently Since Ox is not multi threaded this is the best way to make full use of a multi core processor This option is always cancelled once the run is executed Reset it in this dialog as required The usual estimation results are written to a text file identified by the run number Import this text to the results window using the command File Load Text File If the specifications are stored as a named model in Model Manager before running the new process the associated values and listings can also be imported A tsd data file is created with the usual outputs Import the data by RE loading the model in Model Manager Also the estimates can be loaded for further processing by the command Restart Load Text Input The name and path of the file to load is given in the results window If the option Delete Temporary Files on Exit is checked the temporary code and listing files created by this option are deleted at closedown Results files are not removed and must be deleted by hand as required 8 8
45. Bunzel 2000 The method selected here is used for equation standard errors and also Wald and LM tests M statistics use HAC and nonparametric tests of I 0 see Actions Compute Summary Statistics use HAC Whittle estimates use HAC if KVB is selected The KVB estimates correspond to HAC using the Bartlett kernel and bandwidth equal to sample size Note that they are inconsistent but yield 107 James Davidson 2008 23 asymptotically pivotal tests based on a nonstandard distribution P value inequalities are reported from the published tables and are identified in the output with the 2 symbol KVB can be implemented for nonlinear models and GMM at the user s discretion but take care to note that asymptotic distribution results for these cases are not available to date See the citations in the main document for further details HAC KERNEL FORMULAE AND BANDWIDTH 24 25 26 27 The kernel formula selected here is used when the HAC covariance matrix 1s selected It also determines the choice for Phillips Perron KPSS and RS tests and Fully Modified Least Squares estimation It does not effect the kernels used in density plotting and nonparametric regression which are Ox defaults and cannot be changed by the user There are three options for selecting the HAC bandwidth Manual selection using the scroll bar i The automatic plug in method due to Andrews 1991 The automatic plug in method of Newey and West
46. Dynamic Equation and Davidson and Hashimzade 2006 Note that this feature is experimental GARCH PARAMETERIZATION 9 10 As the default GARCH coefficients are reported in ARMA in squares form in which delta L and beta L in equations 2 and 3 are the AR and MA components In this case the coefficients are named GARCH AR1 GARCH MA1 etc etc Optionally they can be reported in standard form corresponding to the representation of Bollerslev 1986 In this case the coefficients named GARCH Alphal etc are the coefficients of beta L delta L and GARCH Betal etc denote the coefficients of beta L Note E Roots of the GARCH AR polynomial are not reported when this option is checked a The EGARCH model does not strictly have an ARMA in squares representation The default corresponds the stated form of equation 3 The Bollerslev form is the one more commonly reported A It is the user s responsibility to match starting values to the convention selected The GARCH intercept can also be computed in two different ways By default it is omega in equations 2 and 3 By unchecking the box Specify Type 1 GARCH Intercept kappa omega beta 1 will be 122 O James Davidson 2008 computed instead see equation 44 ff of main document OPTIMIZATION SETTINGS The following options should not normally need changing but the defaults may not suit all cases Experimentation is recommended if i
47. E EEA EE EVE ESEE EOS EEEE EEEN EE EEEREN 128 DESCRIPTIONS e n E err EAEE E E EE A EEE T A A AT AEE RES 128 REGISTRATION Si aa Earr E EEA e EEEE rE TE N N E EEE ini E a a 128 10 Interpreting the Output e a a RRR a E 130 PARAMETER LABELLING e ere a ETE E EE ERE Innata ii 130 PARAMETER ROOT TRANSFORMATIONS 1 00 ceecceeceeeseeceseeeeeeceeeeeeneeceeeeeneecetnesenaeees 130 STANDARD ERRORS TEST STATISTICS AND P VALUES ocooccooocccocccconnnconcconnnncnnacanos 131 SELECTION CRITERIA AND SUMMARY STATISTICS 000 ee ce ceeceeseeceseeceeceeneeenaeeeeee 131 CONVERGENCE ISSUES vivvssecsstasecstiscscep E a a a E E E T AN O RE TR RR 132 GRAPHICS FOR REGIME SWITCHING MODELS 0 cece eeeeesceceseeeececeeeeeeneeceeneseneeees 132 BOOTSTRAP AND SUBSAMPLING P VALUES eeeccecsseeeneeceeeeeeneeceseeeeneecenneeeneeees 133 LL Directories and PUES acca ance tocevs Sous sronaconacrveyshtasdaeagdaesteenateyuoed aea osi esaea 133 DIRECTORIES Windows folders cc ccccsccesssccessceesceceseeesseceeeeeesseceeeeesseceeeecsaeceeeeeesaeens 133 HEBE Susini alain 134 FIEE TXBES cosilla iones Dania 134 ns A O A eae e apes ee 135 NUMERICAE OPTIMIZATIO Nic oocirtincri diaria iii iia 136 CHOICE OF SYSTEM ESTIMATORS orri necnon aare ia aR ar EE a 137 USING THE RESULTS WINDOW AS A TEXT EDITOR ooooccccocccoccnnonnnnonccnoncnnnncccnncnnnnccnno 137 ENTERING DATA BY HAND ronet rir a N R a e E 138 MAINTAINING AND EXPORTING PROGRAM SETTINGS coooccccccccnonnconnnonnnncinncconen
48. E S 12 14 SYSTEMS OFEQUATIONS kht ar E E A E A E E 13 15 OUTPUT CONVENTIONS i ana a E E e E S S 13 0 2 How Tocina A a at tan E A 14 HOW TOLOADA DATA SET 00 t becca seb n ae e i n e aaee aS akie 14 2 HOW TO PLOT DATA SERIES cui a da SEEE aE 14 3 HOW TO RUN A SIMPLE REGRESSION occcccccccncnnnnnnnnnnonononononnnonononononnnnnnnncnononononinininons 14 4 HOW TO GENERATE QUARTERLY DUMMIES ooccccccccnnonononnnonoconanananononcnnononnnoncnconanannns 15 5 HOW TO TAKE LOGARITHMS OF YOUR DATA oocccnccnononononononononononononononoconononininones 15 6 HOW TO TEST THE SIGNIFICANCE OF THE REGRESSION c ccccccccoconononononononinonononons 15 7 HOW TO TEST FOR A UNIT ROOT ooooccccnnnnnnnonononononononononononononononocononononononononoconononenonenes 15 8 HOW TO ESTIMATE AN ARMA p q MODEL occooccccoccncoocconnnnonncconononnncconononnncconanonnnccnneos 15 9 HOW TO FORECAST WITH AN ARMA ARIMA MODEL cccccccccnnncnonononononononononinononon 16 10 HOW TO ESTIMATE A SIMPLE VAR MODEL cccccccncncnncnnnonononononononononononononinininininons 16 11 HOW TO ESTIMATE A GARCH MODEL cococcccnnnnnononononononononononononononononinononononocininones 17 User Intertace nennen naa Sec B esha utes de de eae bea E 18 Teal Thies Menus ieiei vnc aiken cere a aia ene eh entice ete os 18 1 James Davidson 2008 1 2 Status Bar and Tool Bar ononnnncnnnnnnonononaninocncnnononenannonoconcnnonanononicccccnonanass 19 1 3 The Results WINdoO Wisin ita 20
49. E a NE TT R E 112 8 4 Options Simulation and Resampling ooocooccccnocccnnnnncnoncnononcnonnnccnnnnccnnnnnon 112 SIMULATION OPTIONS rociar dee voviteerocestniens RTE a E EEEE 112 SIMULATION PRESAMPLE MODE nrnna aa EA E EERS EE ERa 114 TY PETFRACTIONAL PROCESSES iie ao aaea R e EE A AA seat 114 INFERENCE BY RESAMPILIN Ge err eo aa eaa E E A A EE iii 115 RESAMPLING CONFIDENCE INTERVALS ooooocococcconononnnccononoonnnconcnonnnnnonnnnonnncnnoconnnnnnnccnno 116 NEWTON RAPHSON ALGORITHM ceeccecssecesececesecesececeeeeeneeceeneeenaeceeeeeneeceeneeeneeees 116 8 5 Options Graphics sissen ieinter es sesedata updadevanedeaassacedencessaedes 116 GRAPHICS FILE FORMATS ree a o a setbacks ecb da Seba ssn ben de seais beta 116 DATES IN PLOTS raider anes ines Sone eE E ETa acid dades eat a dis 117 BITMAP DIMENSIONS cirea tie inrter e nta a te canes de svbans T e sti a E EE aE 118 ACTUAL FITTED RESIDUAL PLOTS inisini ici enese ieaie aota e D e ia ENEE EEEa 118 CONFIDENCE BANDS Sienra a EE e E ER RAAS 118 MULTIPEE SERIES DISPLA Veco E O EER A a E 118 LINES AND SYMBOL Sordin a a a E A a aA 119 LEGENDS 0 a aia 119 CRITERION PLOT Szenen e a aa te E R 119 DENSITY PLOTS nrin aee A sn 119 LINE STYLES nuren a r E AN SR ERER E 119 SCATTER PEOT OPTIO NS id 120 8 6 Options ML and Dynamics ooocoooccccnocccnoncnononcnonnncnononononnnnnnnnncnnonnncnnnncnnnnnnnns 121 4 O James Davidson 2008 ML PARAMETERIZATION cone 121 DYNAMIC MODEL SETTINGS rece ceecec
50. EMS OF EQUATIONS Setting up a system of equations is greatly simplified by requiring that the right hand side of every equation has the same specification In this way only one specification has to be created and stored This is the natural approach for an unrestricted VAR for example To have the equations different from each other e g with identifying restrictions imposed the method is to create an inclusive specification of which all the actual equations are special cases and then fix the surplus parameters at zero in the Values dialogs enter O in the value fields and check the Fixed checkboxes While editing values one can switch easily from one equation to another using the Next Equation button or the choice widget on the tool bar Parameters fixed at O are not reported in the output although those fixed at non zero values are listed as such Systems of coded nonlinear functions can be estimated in the same way While their specifications can differ each has the common set of named parameters assigned to it fix the surplus ones in Values Equation so that the search algorithm ignores them Simultaneous equation systems can be specified by including variables as both dependent variables and Type 1 regressors When their presence in both sets is detected by the program the system is estimated by FIML It is the user s responsibility to ensure that identifying restrictions are imposed on the equations in this case I
51. INGS 9 10 The default font size of 12 points should suit most monitors but can be changed This setting also effects the help pages whose widths are increased to accommodate the larger text The results window is resizable by dragging the corner with the mouse TSM output can be echoed to the console as well as appearing in the results window To enable this behaviour check the Echo Results to Console box Output from Ox not under the control of TSM such as error messages will also to appear in the console window 126 James Davidson 2008 11 12 13 Tool tips appear by default when the mouse pointer is passed over the tool buttons These can be optionally switched off If the Enable Error Recovery option is checked the default the program restarts automatically in the event of a crash Ox error Note that the Ox error message appears in the DOS console Drag selection allows the quick highlighting of a block of adjacent variables in any list allowing multiple selection Select a variable as usual then put the mouse pointer on another variable and drag briefly hold down the mouse button while moving the mouse These actions select all the names in between Deselection works the same way The option can be switched off in case it fails to operate smoothly on particular systems LINEAR REGRESSION MODE 14 To simplify the user interface for teaching purposes the options for nonlinear estimation by num
52. INTEGRATING REGRESSION ri En E EARE ARREA TE NE aa 59 4 2 Model Dynamic Equ A A A 60 ESTIMATION CRITER A Sucia o 61 MODEL SPECIFICATION coc AS 62 2 James Davidson 2008 VARIABLE SELECTION 0 62 LINEAR REGRESSION seinir eninde evs olen eagen cad loteo dende identidad 63 BILINEAR MODEL cucuta eee lidades 63 NONLINEAR MOVING AVERAGE SPS cccccccessssecseseeeecesececessaeeecseaeeeeseeeeenesaeeeesenaeenees 63 OTHER MODEL FEATURES cr hated ct ies 64 SYSTEMS OF EQUATIONS Fae tecsvees Bho td tani hath Ravina 64 ESTIMATING TYPE I V ARFIMA PROCESSES oocococccconnnonononononononononnnoncnonnnnnccnnnnnnccnnnnnnno 65 4 5 Model Conditional Variance sxc sicca scgsuesseictcvesscasctssinass cies sada asedctedsacsanteas eneed 65 MULTIVARIATE GARA a a a E aE E Mecsas 66 ACA Model Coded PA s 67 METHODS E EA EEE E A S 68 INTERACTIVE CODING eeen e enpe ereere ts e E a Ep ERREA EE EN Ee EE ea 68 TY PES OF FORMULAE ee r eae a E E AE eA Ep eaen EAE e EEEE EEN 68 TEXT BOX CONTROLS cintia ta a tit lat 70 PARSING THE MODEL fc cesses sceesses debidas cido data nai cs dida ED EE Ea A AREA aii EENE 70 PARAMETER NAMES oc ctoccooooinccrododo e eree A T a ea e Er an Epa Enea p ciedad dro 70 VAREA BILE NAMES e a a aE ET EEEE iT 71 OX CODING a E E E T A had 71 4 5 Model Regime Switching lisina aaa 13 4 6 Model Parameter Constraints sss ccsiceciccdiviiivatatelaccadsrehcdbuvetencievigied eateuei lereeese 75 REGRESSOR SIGNIFICANCE TEST eenei irie ie
53. M are conventionally regarded as minimizing a criterion while the ML options are maximands This can lead to confusion especially when interpreting the model selection criteria The optimand for least squares and LGV is reported for comparability as the Gaussian log likelihood a monotone decreasing transformation of the sum of squares but the GMM optimand has no such counterpart By default all the estimation criteria are treated as maximands so GMM criterion The Report Minimand option reverses the signs so Log Likelihood The important issue is that the selection criteria are always signed in the same way as the estimation criterion and so are to be minimized maximized if this option is checked unchecked NUMBER OF GRID POINTS Ze Enter an integer value here to choose the density of points computed in a grid plot If N is set then N 1 points are evaluated in a 1 dimensional grid or N 1 42 points in a 2 dimensional grid Note that grid plotting must be enabled in Values Equation and the run launched with Actions Plot Criterion Grid Set the grid bounds s in the relevant Values dialog s 123 O James Davidson 2008 BOUND ON DYNAMIC PARAMETERS 3 The absolute bound on dynamic parameters controls a penalty applied to the criterion function to prevent extreme values The penalty is applied only to dynamic parameters ARMA and GARCH coefficients and ARFIMA FIGARCH d This is mainly to prevent e g inv
54. NTE CARLO SETTINGS 15 16 17 18 The default number of replications is 1000 Select either the mean or the median of the Monte Carlo distribution for reporting In the former case 2 standard error bands are also shown in the plots and in the latter case the 2 5 and 97 5 quantiles are shown To select the simulation mode and change the random number seed see Options Simulation and Resampling The scroll bar allows selection of one of the forecast periods for a density plot Note that the maximum selection varies with the setting for number of forecasts ACTUALS IN FORECAST PLOT 19 It is usually helpful in a post sample plot to show some but not always all of the series for the estimation period The default is to include the last 50 observations This can be changed and to include all available observations simply enter any value large enough Note that when the forecast period includes or overlaps the data period as for ex post forecasts the actual values are always shown 111 James Davidson 2008 CONFIDENCE BANDS 20 By default confidence bands are enabled It may be desirable to switch them off if for example a user coded function contains lagged adjustment These dynamics cannot be taken account of in the analytic formulae which will therefore be incorrect PLOT DISPLAY 21 Ex ante forecasts can be viewed by listing values in the results window see Options Output and Retrieval o
55. OW TO TEST THE SIGNIFICANCE OF THE REGRESSION x The following procedure provides a valid time series implementation of the F test of the Regression reported routinely by many packages It tests all exogenous regressors but automatically excludes the trend seasonal dummies and lagged dependent variables from the test set Thus the null hypothesis can be a valid univariate representation of the dependent variable In the Linear Regression dialog check Wald Test of Constraints Use the button beside the checkbox to open the Constraints dialog and check the box Test Joint Significance of Regressors The test is computed by running the regression or by choosing Actions Compute Test Statistics Wald Test of Set Restrictions 7 HOW TO TEST FOR A UNIT ROOT X XX XA Open the Setup Compute Summary Statistics dialog Check the Report I 0 I 1 Tests checkbox Choose the variable you want to test and press Go The Augmented Dickey Fuller test and Phillips Perron statistics are among the results reported The order of lags in the ADF test is chosen automatically to optimize the Schwarz model selection criterion over the range up to M O T 1 3 The bandwidth settings for the Phillips Perron test can be changed in Options General 8 HOW TO ESTIMATE AN ARMA p q MODEL x Click the Space Shuttle button on the tool bar to open the Dynamic Equation dialog If this is not shown open Options General check Enabl
56. Post 1 step forecasts are simply the fitted values of the model using actual values of all lagged and explanatory variables for the selected forecast period This cannot exceed the available observations so the estimation sample must be set appropriately By default the forecast period for ex post forecasts is set to the maximum available observations following the Last Observation set in the Setup Set Sample dialog If this setting is changed the number of forecasts is adjusted to the default To include fewer than the maximum number of observations in the forecast period change this setting after setting the estimation sample Ex post forecasts and forecast errors are displayed in the Actual Fitted and Residual plots The main purpose of this option is to check model stability Two test statistics are computed appropriate to short and long forecast periods respectively The chi squared short period test Forecast Test 1 is the generalization of Chow s 1960 second test and depends on the additional assumption of Gaussian disturbances under the null hypothesis The second test reported depends on the model In single equation linear regression models Chow s stability test statistic is reported choose between F and Chi squared forms by checking the box in Options Tests and Diagnostics In other cases where the need to re estimating the model for sub periods precludes generalizing the Chow procedure a difference of means
57. The bandwidth used to compute the GPH bias test see Davidson and Sibbertsen 2006 should be set to the maximum T 2 to test the hypothesis of a pure fractional process Use this setting if in doubt Setting the bandwidth to CT beta for 4 5 lt beta lt 1 yields a test of a more general hypothesis allowing any short run dependence that does not induce bias Note that the test is inconsistent with beta lt 4 5 8 The choice of MS Fourier order is also a trade off between bias and efficiency see MS paper for recommendations or experiment 9 The smoothing option available for both estimators uses local non overlapping averages of periodogram points in the regression If in doubt keep this setting at 1 3 9 Setup Cointegration Analysis This dialog allows a Johansen type multivariate cointegration analysis to be carried out on any subset of the data The available procedures are Testing hypotheses of I 0 and I 1 on the selected variables Lag length selection for the Johansen CIVAR by Akaike Schwarz or Hannan Quinn selection criteria 49 James Davidson 2008 x x Johansen maximum eigenvalue and trace tests for cointegrating rank Wald tests of structural exclusion restrictions on the cointegrating vectors including MINIMAL analysis Select the variables to be included and CIVAR options then select the desired procedure using the radio buttons To execute the procedure press Go or the Run or Evaluate
58. The icon without the white square represents the GUI front end running under the Java Runtime Environment Note if TSM is started by clicking on a settings file in Windows explorer the Windows DOS box icon appears instead of the first TSM icon The Windows button remembers which dialogs were open between sessions Pressing it at start up restores the window configuration existing at a recent close down To avoid an excessive clutter of dialogs getting re opened the configuration is reset if the time lag between sessions exceeds 11 hours When lengthy computations such as optimizations recursive estimations grid plots and Monte Carlo experiments are running a Stop button appears on the tool bar Clicking the button opens a choice box with the choice of aborting the run or continuing Note there may be some delay before the box opens 1 3 The Results Window The text area is editable Comments and aide memoires can be typed in and saved with the output Text can be highlighted with the mouse hold down the mouse button and drag the I beam cursor and then cut or copied to the Windows clipboard Use the right mouse button to open the context menu The command File Save Selected Text allows highlighted text to be written to a named file The results for an estimation run are printed with a heading showing the version number of the program a run ID number incremented before each run and the date and time The ID numbe
59. Time Series Modelling Version 4 25 User s Manual James Davidson 28 February 2008 This document is also accessible through the program Help pages Contents Wiats NeW trauma rales danita 6 PES MEADS ii nd 6 TSMAZlA ti o ad SOP SB IR de cOn 6 SMA a sched caabesseaescatas cadcassevscuheas chad oe eten heen cadioesesat a 6 A Ro AY A Meet Sec eth As est oe cet ane vo Pacha Riese i a tl nr elo eres cca 6 SESIMEA O aA unc alee os not etal ook 6 il SSS Eo 0 Ieee aa a o a APRS RE nO o e PES 7 TS MA Di AS IE SOR OO oR Ao ER I SO AA 7 TSMA dimarts dina a A 7 PSA de ERE ee oda cado ne 7 TSMAMO LN O OA 8 ESMAS e e a le a Ad o le a 8 O Introduccion dai 9 DA TSMB as rana cds ds 9 I ENTER INGDATA ici di ii bd a de oad de Ses ban Bees ta de Ai i 9 2 MENUS AND DIALOG 0 dra 9 3 COMPUTING ESTIMATES TESTS AND FORECASTS ooccccccccncnnncncncncncnnnonononeninininicicinos 9 4 SAVING PROGRAM SETTINGS conooococonononononononononononononononononononononononononononononononononononononono 10 5 ORGANIZING YOUR WORK oocccccccccnonononononononononononononononononononononononononononononononononenonenes 10 6 SMU A O Na 10 MODELS 0 idas 10 8 PROGRAMMING WITH TS Moococcccncncnnononononononononononononononononononnnnnnnnnnnnnnnnnnonononononcnnnnanananes 11 9 TYPES OE MODEL ii 11 10 SEEECTING VARIABLES cui ta 11 11 VARIABLE TY PH ts 12 12 PARAMETER VALUES 40d ti 12 13 CODED FUN OTON S 00 Aeiceds oscasccccieoecs ost caccseseoes es sat E a E E
60. Type Export Listings to Files of Type Save Listings Automatically Print in Results Window Retrieve Generated Series Test and Diagnostics XK LX LK LK EX E X XX Q Test Order Q Test Type LM Tests Durbin Watson Test Diagnostic Tests Covariance Matrix Formula Kernel for HAC Covariances Bandwidth for HAC Covariances Show Residual Moments Show Log Likelihood amp Criteria Tests in R42 Form f Use EDFs Forecasting Options o Forecast Type Forecast Method Actuals in Forecast Plot Monte Carlo replications Compute Confidence Bands Impulse Responses Simulation and Resampling Options x Shock Distribution 101 XLS None No Correlograms Once 12 Box Pierce No No None Robust Parzen n 1 3 for Bartlett n 1 5 otherwise Yes Yes No No Ex Ante Multi step Analytic 50 1000 Yes Impulse Gaussian James Davidson 2008 XK XX AX XK XA LK LX O Random Number Seed Shock Variance Gaussian Presample Data type I fractional Use Likelihood Model Enable Bootstrap Inference Once Always Confidence Intervals Bootstrap Replications Fast Double Bootstrap Bias Correction Newton Raphson algorithm Maximum Iterations Graphics Options Export Graphs to Files of Type Save Graphs Automatically Display plots using GnuPlot Dates Format PNG Image Size 2SE Band Style for Forecasts Multiple Series Display Time Series Plot T
61. Variance and Values Distribution dialogs In this case the setting of Shock Variance is ignored By default the sieve AR method used an increasing function of sample size as maximum lag order For this case enter 1 in the Max Sieve AR Lags text 113 James Davidson 2008 field Setting a zero or positive value over rides the default Setting 0 1s equivalent to the regular bootstrap method 9 If bootstrap is selected and the random number seed is set to 1 the shock generation procedure returns the actual model residuals in original order The generated series should then be identical to the original data series apart from possible rounding error This feature provides a check that the simulation module is inverting the fitted model correctly Note that to generate Markov switching models also requires a latent switching process so this check will be valid only if the Markov transition matrix is fixed at the identity matrix 10 The option wild bootstrap skewness sets the parameter a such that the t th drawing is e u_t where u_t is the sample value fixed and e a and l a with probabilities 1 1 a12 and a 2 1 a 2 respectively Note that this setup preserves the first two marginal moments of the distribution The default is a 1 which always yields a symmetric distribution but preserves kurtosis Setting a 1 618 preserves the original skewness if any but doubles the kurtosis The value of the Kolmogorov Smi
62. ads and differences 2 The sample count is initialized at the first line of the data file not the first available non missing observation 3 The All Available Observations button is useful to check for missing observations The largest sample available for all the variables in the currently specified model is selected The actual sample used for estimation is in any case restricted to this set 4 This dialog can also be accessed from within other dialogs controlling functions where a sample must be specified Five different sample selections can be set concurrently for different program functions The sample set depends on where the dialog is opened from The locations are Setup Recursive Rolling Estimation Sample 1 Setup Summary Statistics Sample 2 Setup Nonparametric Regression Sample 3 Setup Semiparametric Long Memory 3 Sample 3 Setup Cointegration Analysis Sample 4 Model Linear Regression Sample 1 Model Dynamic Equation Sample 1 Graphics Show Data Graphic E Sample 5 The function of the dialog when opened from the menu bar depends on which dialog is currently open By default it sets Sample 1 5 Sample selections 1 3 and 4 are stored as part of a model and retrieved by reloading the model Selections 2 and 5 are saved with general program settings 6 Click the Simulate button if the sample is being set for a simulation run not for estimation In this case th
63. ae see Section 1 5 Parameters can be written in the notation a i where i is the number appearing in the left hand column in the Values dialogs p i A 1 and P i are all permitted variants but the square brackets are mandatory note CAUTION Parameters can also be identified by name However some parameters are named differently in the Values dialogs and in the output If in doubt use the number notation which is unambiguous Suppose there are P restrictions Using the numbering notation 76 O James Davidson 2008 described in Section 1 5 in practice parameter names can also be used the restrictions must be entered in the solved form a j1 fl a k1 a kM a jP fP a k1 a kM for k1 kM not equal to j1 jP where f1 0 fPQ are differentiable algebraic expressions The program imposes the restrictions by replacing a j1 a jP with the given functions of a k1 a kM 13 Restrictions cannot be entered in implicit form Example a 0 a 1 a 3 a 2 exp a 1 a 4 is OK a 0 a 1 a 2 a 2 a 1 a 3 is NOT valid Not solved form A valid form of the first equation would be a 0 a 1 a 1 a 3 4 7 Model Equilibrium Relations An Equilibrium Relation Eq R is defined as a linear combination of lagged variables that is inserted as a regressor in one or more equations of a system with the combining coefficients being either restricted or estimated This is so
64. al instruments are included to match the lag setting for Type 2 regressors Even if no Type 2 regressors appear 79 O James Davidson 2008 the lag length can be set to control the number of lags of additional instruments By default lagged endogenous variables are not used as instruments If this option is selected with the checkbox lags are included to match the lag setting of the endogenous variables Type s To use lagged endogenous variables as instruments but not as regressors suppress them in the equation by fixing their coefficients at O in the Values dialog Lags can be be created manually for use as instruments in the Setup Data Transformation and Editing dialog However be careful with the automatic lag settings in this case If lags are double counted the instrument matrix will be singular 80 O James Davidson 2008 5 Values 5 0 Values General The Values dialogs are used to operate on model parameters They allow ok x ok setting starting values for the search algorithm fixing parameters at chosen values in the estimation setting bounds on parameters for estimation subject to inequality constraints setting a range for a grid evaluation of the estimation criterion in one or two dimensions selecting parameters for Wald significance tests setting up linear functions of parameters for Wald restrictions tests Unlike the other dialogs having fixed layout Values dialogs can be resized Grab th
65. allows the choice of x x Notes number of regimes type of switching simple Markov switching explained switching Hamilton s model or smooth transition ST which model components to switch specification of the explained switching probabilities or transition function where these options are selected Regime switching is not activated until at least one model component is selected for switching Except for the smooth transition model regime switching requires a time domain maximum likelihood estimator Options are greyed out until a valid selection is made In the Markov and Hamilton models both the matrix of estimated transition probabilities p_ ji and the unrestricted parameters t_ ji with standard errors are reported in the output The latter are labelled Logistic of POI See the main document for details In Hamilton s model the Intercept selection in Models Dynamic Equation is ignored The intercept is specified as shown in the TSM document In the explained switching case the radio buttons allow the choice of variables to explain the probability of switching into the given regime at date t An intercept can be optionally added to the equation Distributed lags are not implemented for switching regressions but the Lag scrollbar allows a fixed lag to be applied to the variable s If and only if the lag is positive the dependent variable s can be included in the set There are two versions
66. alog first click the list o Opens the Graphics Show Data Graphic dialog if no variable list has the focus Double Chart button displays combined chart of actual and fitted values and residuals Only available following an estimation run Optionally can also show the actual fitted scatter and residual histogram and kernel density see Options Graphics ES Dialog 1 and Dialog 2 buttons can be assigned by the user to open any dialog lacking a dedicated toolbar button To assign a button simply open the Options General dialog open the target dialog or command and press 19 O James Davidson 2008 Notes the assignment button see Section 8 8 for details Windows button Toggle action o Restores dialogs in previous positions duplicating Actions Restore Dialogs if dialogs closed o Closes all dialogs duplicating Actions Close All Dialogs if dialogs open Stop button only displayed when an iterative calculation is in progress Pauses the calculation and opens a choice box to Abort or Continue The Space Shuttle and Running Man buttons can be optionally omitted from the button bar deselect Enable Optimization Estimators in Options General This option can be used to simplify the interface for classroom use When TSM is running two TSM icons appear on the Windows task bar The icon enclosed in a white square represents Ox running in a minimized console window Click it to view the window
67. als Monte Carlo simulation of the estimation procedure yields the bootstrap distribution a Subsampling is the method of fitting the model to successive contiguous subsamples of the data set and constructing the empirical distribution of the subsamples It does not involve drawing random numbers 14 The output is available in the form of confidence intervals p values and plots of the empirical distributions generated 15 By default resampling is deselected automatically after a single run Once There is an option to select it permanently as the inference method Always Selection is indicated by a flag on the status line B for bootstrap and S for subsampling 16 The number of replications determines the accuracy with which the p value is measured However because of the small sample error in the p value due to replacing actual with estimated parameters the accuracy attained from a large number of replications is typically spurious The default of 99 implying accuracy is bounded by 1 is probably adequate in many cases 399 would be sufficient in nearly every case 17 The bias correction option subtracts an estimate of the bias from each 115 James Davidson 2008 18 parameter point estimate This is computed as the difference between the mean of the bootstrap distribution and the point estimate estimating respectively the mean of the estimator distribution and the true value The fast double bootstrap is a
68. alue to unity to limit the ratio of largest to smallest parameters effective only if starting values are a guide to the relative magnitudes Setting to a higher value e g 10 inflates all parameter values to reduce the risk of rounding error in the evaluation of numerical derivatives ER Tinker with the simulated annealing settings in Options Optimization and Run There are not many useful guidelines for good choices here in most cases raising the number of iterations cannot hurt but also try switching it off see Note 8 below SA The scaling of the variance intercept parameter in GARCH models can be critical especially in the IGARCH case See Options ML and GARCH for details Experiment with the settings for EGARCH and GARCH M models in Options ML and Dynamics For dynamic parameters AR MA etc experiment with the bounding option in Options Optimization and Run None of these fixes is guaranteed to improve matters but setting starting values to good guesses of the estimates is always helpful For example if it is believed that a unit root exists in ARMA or GARCH models start the AR parameter at 1 rather than 0 Using the Impose Unit Root option in Model Dynamic Equation may help similarly Another good strategy with a complicated model is to simplify it initially by deleting or fixing some components Estimate the simple model then add back the deleted components one at a time The estimates of th
69. arlo experiment Note how a different model can be used to estimate from the simulated data to permit misspecification analysis Whilst the simulation code has been carefully checked there are so many 139 James Davidson 2008 combinations of model features available that it is not possible to guarantee that they will all work together as intended To ensure the integrity of simulation results it is a good idea to run a check on the selected model Users may also wish to check out their own supplied code To verify that a model is being correctly simulated follow these steps 1 Evaluate the model with a data set and chosen or estimated parameters to generate a set of residuals 2 Open Options Simulation and Resampling and select Bootstrap for the Shock Distribution In the box Random Number Seed enter the value 1 This setting causes the simulation to be done with the actual residuals without random resampling 3 Run Actions Simulate Current Model and save the simulation This should match the original series exactly apart conceivably from small rounding errors Compare the series in Setup Data Transformation and Editing Choose Mark for one series then List Edit Compare for the other to see them side by side 4 In a Markov switching model the simulation involves random regime switches To disable these put the switching probabilities to 0 or 1 in the simulation In the case of explained switching models choos
70. be saved in a new named file Highlight any number of variables in the list before giving the command This opens the file dialog for saving provide a new name and type for the file The existing data set is unaffected Make Formula Allows any algebraic function of variables to be computed as a new variable Pressing Go opens the text entry field For information on typing formulae see Section 1 5 Entering Formulae TEXT BOX CONTROLS Cancel Closes the text box discarding changes No variable created Delete Deletes the currently displayed formula clears field Next Displays the next formula if it exists New Opens a new blank formula where there is no Next Previous displays the previous formula if it exists 38 James Davidson 2008 OK Closes the text box and creates the new variable Return Equivalent to pressing OK Closing the text box with the Windows Close button x is equivalent to pressing Cancel Note To evaluate a recursive formula use E j where j is a positive integer to denote the function value lagged j periods Make Seasonals For frequency N create N dummy variables with every Nth observation 1 otherwise 0 Set N 4 for quarterly data N 12 for monthly etc Move Up Move Down Use these commands to re order the variables in the data set Pressing Go repeatedly will move a single highlighted variable up or down as many positions as required Alternatively mov
71. both limiting the maximum number of NR iterations or raising the convergence criterion or both NR is always used for bootstrap iterations The algorithm can optionally be used for Monte Carlo experiments instead of BFGS by checking the checkbox 8 5 Options Graphics GRAPHICS FILE FORMATS 1 The graphics output formats available depends on the platform and the program configuration PNG is a standard bitmap format providing an exact image of the 116 James Davidson 2008 displayed window in the dimensions specified see below IrfanView is an excellent free graphics program for Windows that will display PNGs and also convert them to JPG EMF GIF and other popular bitmap formats a EPS and EPC are vector graphics formats They can be viewed with the free package GhostView which will also convert them to PDF They can be loaded directly into Word and TeX documents and can also be edited in various drawing packages x The GIF option works in UNIX LINUX but does not work currently on the Windows platform If the checkbox Save Automatically is checked every graph is saved to disk in the chosen format at the same time it is displayed Otherwise the menu item File Graphics Save Last Graphic saves the one most recently displayed GWG GiveWin format files are created if the compiler directive DEFINE OXDRAW appears in the run file This option loads the OxDraw graphics package and disables GnuPlot so
72. coefficients are restricted in any relation Ze With two or more Eq Rs note that this dialog specifies the variables to appear in all of them To create distinct relations exclusion restrictions fixing coefficients at 0 must be set up in Values Equilibrium Relations Note For consistent estimation the relations should satisfy the standard rank conditions for identification of a linear system 3 When Closed VECM is checked the lagged variables included in the VECM are the dependent variables LESS the fitted combination of Type 1 intercept and or Type 1 regressors See main TSM document for details of the specification Option C 4 The equilibrium relations are formulated in the Model Coded Function dialog Note that Residual format must be used no in the field This is the only permitted option when option C is selected in this dialog de When Coded Equilibrium Relations is checked and Equilibrium Relations is also checked in the Model Dynamic Equation dialog the Coded Function checkbox is disabled coded functions can appear either in the main equation s or in equilibrium relation s but not both at once 6 The number of relations in the model is determined by the number specified in the Model Coded Function dialog This overrides the setting in this dialog T Formulating the relations with enough restrictions to ensure identification is entirely the responsibility of the user Use this option only
73. commands If the Restart command is given after editing the user s code resulting in a compilation error the program will fail to restart In this event check the console window for error messages TSM can always be restarted using the default shortcut if required This shortcut uses the unchanged copy of tsmod_run ox in TSM HOME 27 James Davidson 2008 11 Use Simple Restart for option changes that require a restart such as hiding showing advanced estimation features 2 1 File Settings Settings files extension tsm save the current state of the program including optional program settings model specifications and parameter values If the option to save the specifications was selected when it was saved loading a settings file recreates the exact state of the program at that time including operational settings model specifications and starting values Otherwise it restores the operational settings only The file settings tsm in the working directory is automatically loaded at start up if it exists It is saved with the model specifications and starting values before each estimation call and also at shutdown The current state can be saved at any time in a named settings file and reloaded subsequently The available commands are Open Loads settings from a selected file Only files with extension tsm can be opened Save Saves settings to the default file settings tsm Save As Saves settings to a nam
74. controls the number of lags generated not the interpretation of the coefficients A GARCH regressor is indicated similarly with an additional G prefix For example G1 Varl denotes that Varl is a GARCH regressor of Type 1 The GARCH or EGARCH or APARCH intercept of Type 2 kappa is indicated with the prefix 2 However no indicator is used for the GARCH EGARCH APARCH intercept of Type 1 omega To indicate the regime in an explained regime switching model the regressor has an additional Rg prefix For example Rg1 Var1 denotes that Varl is a regressor explaining the probability of switching to Regime 1 In smooth transition models the parameters of the single and double transition factors are indicated with the prefix Sm For example Sm1 Intercept denotes the location parameter of the first transition factor The bilinear model is described in the output as Bilinear AR F IMA p r d q where r refers to the selected bilinear order and p d and q are as for the standard AR F IMA model PARAMETER ROOT TRANSFORMATIONS 7 By default the GARCH intercept term is estimated in square root form Correspondingly in ML estimation of models without a conditional variance component the error standard deviation is estimated by default This is for reasons of numerical stability Particularly in IGARCH models where the parameter can be close to zero numerical derivatives can be highly inaccurate with
75. d Dickey Fuller statistics o Check Fully Modified Least Squares to compute the Phillips Hansen 1990 FMLS efficient estimator o Check SSW Efficient Least Squares to compute the least squares estimator augmented by leads lags of regressor differences as proposed by Saikkonen 1991 and Stock and Watson 1993 SSW LS For Instrumental Variables estimation I V 2SLS 3SLS use the Choose Instruments button to open the selection dialog The Sample button opens the Set Sample dialog Use this to select the observations to be used for estimation The setting is the same as if opened from Setup Set Sample Pressing the Simulate button allows the All Available Observations button to show the available sample of exogenous variables for a simulation of the dependent variable The Options button opens the most recently opened estimation options dialog from the Options menu By default this is the Tests and Diagnostics dialog Click the horizontal lt lt lt lt and gt gt gt gt bars in these dialogs to switch between them The Values button opens the equation Values dialog or refreshes it if it is already open To compute the estimates press the Go button This duplicates the Evaluate button on the toolbar and the Actions Run Estimation menu item For models specified in this dialog the estimates are computed by the usual analytic formulae Equations specified in the Model Dynamic Equation dialog are est
76. d Diagnostics If the Moment Test option is selected the selected HAC formula is used to compute this covariance matrix This selection implies that serial correlation is permitted under the null hypothesis Select the F form of the test with the checkbox 6 Perform the test immediately with the current values by pressing Go Otherwise it will be performed following the next estimation run Cancel it by pressing Clear WALD TEST OF SET RESTRICTIONS T This option does not open a dialog but simply computes the test of the constraints currently specified in Model Constraints and the Values dialogs The option allows new constraints to be tested on the current estimated model without re estimation If no constraints are specified it does nothing SPECIFIED DIAGNOSTIC TESTS 8 This command evaluates the optional tests that have been specified in the Options Tests and Diagnostics dialog These are computed automatically following an estimation or evaluation run but this method allows additional tests to be computed without generating the complete estimation outputs TEST FOR I 0 DEPENDENT VARIABLE 9 This option simulates the model currently stored and computes Breitung s 2002 statistic for the partial sums The reported Kolmogorov Smirnov 91 James Davidson 2008 statistic compares the bootstrap distribution of this statistic with the same statistic computed for the corresponding 1 1 d shocks Its object is to check w
77. d Equations If both options are selected this one is over ridden OTHER MODEL FEATURES 19 20 21 22 23 24 The selectable model features are conditional variances ARCH GARCH coded functions regime switching equilibrium relations and constraints Select these features to be included in the model with the checkboxes at the lower left side of the dialog If a feature checkbox is greyed out disabled this means that the feature is unavailable with current settings usually choice of estimator For example conditional variance models need an ML estimator to be selected Also Coded Function is greyed out if coded equilibrium relations are specified in the Equilibrium Relations dialog For this case the Coded Function dialog is dedicated to specifying equilibrium relations Model features generally require options to be set in the corresponding dialogs to be active It is not possible to select a feature with the checkbox unless some model options have been set Click the square buttons to the left of the checkboxes to open the corresponding dialogs If options are set these buttons are highlighted The dialogs can also be opened from the Model menu NOTE Values dialog s corresponding to model features equilibrium relations switching regimes are not accessible unless the feature is checked To compute a Wald test as part of the run as well as to estimate subject to constraints the Parameter Constrain
78. d otherwise of Type 1 NOTE test variables cannot be assigned to a Type for which lags are already selected If lags are specified for Type 1 variables the test may be unavailable A warning message is printed in this event The AR common factor test is enabled in the following case a model with Type 1 regressors current values only no Type 2 regressors and an AR p error process is specified but not a fractional process The null hypothesis is that p lags of the regressors are not independently significant in other words that there are common AR factors shared by the dependent variable and regressors in the model so that AR errors are valid representation of the dynamics The T R22 form option gives a choice of small sample approximations for diagnostic LM tests on the mean model The default is to report the 105 O James Davidson 2008 statistic W 1 W T where W is the usual LM statistic and T is the sample size If W takes the usual form of TR 2 in the artificial regression of the residuals on the gradients under HO the default is therefore TR2 1 R42 In a linear model this is equivalent to normalizing the statistic with the unrestricted residual variance under the alternative Note that the asymptotic distributions are the same under HO Select the option to report W itself When the F form of the statistic is selected this option is unavailable CONDITIONAL MOMENT CM TESTS 10 11 12 13 Five con
79. d plotting None also effected by turning off calculations in Options Forecasts Bands additional lines are plotted to show 95 region Bars the default 95 confidence region marked by vertical bars Fan coloured bands mark six different confidence regions around the point forecast The confidence levels are 40 yellow 60 ochre 80 brown 90 mauve 95 light purple 99 dark purple Notes on fan plots l Reversing the colour bands is a setup option see Appendix B 2 Fan plots cannot be combined with other plots or other graphs in the same frame This is a Gnuplot limitation The pre forecast actuals series is plotted as a zero width band coloured dark purple no symbols 3 Fans are not available for monochrome plots or recursive forecasts The default option bands is used in these cases MULTIPLE SERIES DISPLAY 12 There are three ways to plot several series at once E Individual each plot in its own frame di Separate plots in the same frame default E All series in the same plot 118 O James Davidson 2008 13 The last option can also be selected in the Graphics Show Data Graphic dialog in which case the style of each line is selectable Note the option to plot the last selected series against the right hand axis in this case If a system is estimated the above three options are available for plotting the series associated with each equation actuals fitteds residuals etc If the I
80. de Your program can call the main program functions such as Run_Estimation and Run_Simulation and perform further operations on the output The special scripting language is fully detailed in the programming manual To see what your current set of non default options looks like in coded form give the command File Settings Display Save Text and inspect the listing created The reverse operation is also possible Write out a set of coded commands in the TSM launch file and these options are then set when the GUI program is started This provides an alternative way to set and maintain your list of favourite program options KKK K K K K K K K K K K K K K K Modelling with TSM KKK K K K K K K K K K K K K K K 9 TYPES OF MODEL There are two main model specification dialogs called respectively Linear Regression and Dynamic Equation The regression scatter and space shuttle toolbar buttons give direct access to these The latter can be optionally hidden to simplify the interface if these features are not being used Linear Regression is used to specify linear models for estimation by a closed form expression or at most a fixed finite sequence of calculations These include OLS 2SLS SUR and 3SLS Although linear regressions can also be specified in the Dynamic Equation dialog its special role is to set up nonlinear dynamic models All estimation in this dialog even of linear models is done by optimizing a log likelih
81. dialogs Checkboxes To turn program options on and off Radio Buttons To choose from a set of mutually exclusive options Choice Widgets To make a choice from a list of mutually exclusive options Scrollbars To input numerical values usually integers e g sample size Text fields To input strings of characters from the keyboard These may represent names to label the output or real numerical values Lists Columns of names usually of data series that can be selected and deselected with the mouse Notes 1 In model specification dialogs the choice of radio button may determine the interpretation of list selections The correct sequence of actions is Click the radio button to select the type of variable Click list items to select deselect them To avoid unintended choices it is a good practice before launching an estimation run to click each radio button in turn and note which variables are highlighted in the list for each case 2 Choice widgets are similar in function to radio buttons convenient for larger numbers of alternatives The widget shows the current selection in the window Click the down arrow to display the list which can be scrolled if necessary then click the desired selection 3 Lists are equipped with vertical scroll bars when there are more items than can be displayed at one time Drag the bar to bring then into view 21 James Davidson 2008 Horizontal scrolling allows long names to be view
82. dialogs a test of the fixing restrictions is generated This scheme allows testing of one set of restrictions 108 James Davidson 2008 while simultaneously including others in the maintained hypothesis NOTE This option is not available for linear regressions Use Wald tests to test restrictions in this context SUPPLYING AN EDF FILE FOR P VALUES 30 31 Check the box Use EDF from File for p Values if tabulations of test distributions has been created by Monte Carlo simulation of the null hypothesis The currently loaded EDF file is used to supply p values for each test for which a tabulation exists in the file In the case of significance tests t tests the parameter s name must match a name in the file Notes 1 P values taken from the EDF are marked with a in the output 2 See Setup Monte Carlo Experiments for details of the EDF file format 3 EDF files can be read and plotted in Setup Look Up Tail Probability and Setup Look Up Critical Value To read off a p value type the test statistic into the first Tail Probability dialog 4 EDF files are spreadsheet files recommended format is xls They can be loaded as data files inspected and merged in TSM If tabulations for several sample sizes are created these can be merged into a single EDF file Use the command File Data Tabulations Merge EDF File to merge a file on disk with the one resident in memory These tabulations will be used to calcu
83. directory Reset it by the 133 James Davidson 2008 command File Results New Results File navigate using file dialog or the command File Results Locate Results Folder type path in the text field FILES These files may be created by TSM4 in either the Start in or Results directory S indicates that a file can only reside in the Start in directory Otherwise it will be created in the Results directory if that is different C indicates that these file names can optionally be changed for a particular installation by editing the file tsmgui4 h settings tsm S C registration txt tsmod_run ox S C usercode ox S C errchk S FILE TYPES tsm txt Contains all the user s settings and specifications including the most recent estimates and stored model specifications Saved automatically before estimation or simulation runs and at closedown Contains the user s licence code By default this is written to the TSM Home directory subject to the user having write permissions and there being no pre existing licence file there Otherwise it is written to Start in directory or if this also contains a licence file to the current results folder This allows multiple licenced users to share the same installation NOTE The program looks for registration txt in reverse order first looking in current Results directory then in Start in if this is different and finally in TSM Home The registered
84. display within the program is not available The format settings in this dialog are ignored See the main documentation for more details Checking the option Monochrome Plots yields graphics suitable for reproduction in black and white Coloured lines are replaced with patterns solid broken dotted etc In Windows these patterns can be edited by clicking the top left corner of the Gnuplot display window and choosing Options Line Styles Files with extension PLT are created by GnuDraw for processing by GnuPlot These are text files that can be edited for further processing if you know the GnuPlot command language If the box Keep PLT Files is checked these files are retained in the results folder after creating a graphics file Otherwise they are deleted automatically DATES IN PLOTS 6 By default when observation dates are specified they are displayed on the time axes of plots in the format YYYY the year Other options are to show month and year in the formats MM YY or MM YYYY and to display observation numbers No Dates NOTE With daily weekday data the date indication is generally approximate since there is no allowance for missing days such as holidays However in most daily data sets with large numbers of observations the axis labels will be an adequate approximation If individually dated weekly daily observations are plotted the dates can be shown in the additional formats DD MM Y Y or YY MM DD as w
85. ditional moment tests are pre set The hypotheses under test are the following X Autocorrelation correlation between current and lagged normalized residuals g Neglected ARCH correlation between current and lagged squared residuals l Nonlinear Functional Form correlation between the normalized residuals and integer powers of the fitted values Heteroscedasticity correlation between the squared normalized residuals and the squared fitted values x Test for AR common factors correlation between the normalized residuals and lags of the Type 1 explanatory variables see para 9 above l Information Matrix Test expected value of the difference between the information matrix and outer product of the score Note that in GARCH type models CM tests use the normalized variance adjusted residuals as the test covariates In tests for neglected ARCH at least fourth order moments must exist and failure of this assumption can invalidate test results caution is advised when interpreting the findings CM diagnostic tests are always computed with the joint covariance matrix of scores and moments computed by the robust method see 12 below Moment tests can also be specified using one of the HAC estimators see Actions Compute Test Statistics Moment Tests The CM and LM tests are unavailable for use with the Whittle estimator The information matrix test is also unavailable with the least squares and GMM options since the de
86. e Available Sample to be checked corresponds to included regressors only ignoring the dependent variable to be simulated dl The button is highlighted when the option is selected Cancel 1t by clicking again or by closing the dialog The button is disabled unless the dialog is opened from either the menu bar or one of the Model dialogs 36 James Davidson 2008 3 2 Setup Data Transformations and Editing In this dialog data series can be edited renamed deleted and created through as dummies or by transformations of existing variables The data can be rearranged sorted reversed and and written to new files The commands are arranged under the two headings editing and transformation x Press either Edit or Transform buttons to bring up the desired list of choices Use the choice widget to choose the desired operation or transformation Scroll down to see the full list of options for details see below To execute an edit command or transformation either highlight one or more variables in the list and press Go or just double click a variable To mark a variable highlight it on the list and press Mark To remove the mark press Mark with no variable highlighted If changes are made the Save Modified Data button is enabled Use this to open the choice box for for saving either to the original file or as a new file EDIT COMMANDS Note commands marked with do not operate on individual variabl
87. e line widths and 8 selectable line style options for series plotting TSM 4 22 Kiefer Vogelsang Bunzel KVB inference with inconsistent covariance matrix estimation TSM 4 21 F Nonlinear moving average SPS model feature providing close approximations to STOPBREAK and STIMA models gt Recursive coded equations can include the lagged value as an argument Extended options for coding nonlinear models including nonlinear ECMs and nonlinear MAs using the recursion feature Panel to create edit view a model description Text is saved with the model ES Forecast confidence bands now plotted in system forecasts System impulse response option 6 O James Davidson 2008 TSM 4 20 Automatic regressor selection by optimizing info criterion Local Whittle ML long memory estimation Nyblom Hansen model specification tests Coded nonlinear equilibrium relations Supplied EDF option for critical values extended to Ox coded test statistics Text files can be loaded into the results window for editing Restart option for one click incorporation of changes to user s Ox code F Randomized coded simulation models XK XA X TSM 4 19 F A formula parser enables three new features o Algebraic data transformations o Nonlinear parameter restrictions replaces existing procedure o Nonlinear equation estimation complements the existing ability to compile Ox functions into the program More limited in scope but m
88. e parameter values large enough to ensure that the switching probabilities are either O or 1 for nearly all values of the explaining variables Don t forget to reset the random number seed afterwards Should a flaw in the simulation code be suspected please notify the author STARTING TSM FROM WINDOWS EXPLORER 23 24 Double clicking on a TSM settings file with extension tsm and red TSM icon has the same effect as starting the program from the Start menu and then loading the settings with the command File Settings Open The Start in directory is in this case the directory where the target TSM file resides Any data file having a supported format can be selected in Explorer and loaded into TSM In this case right click the file with the mouse and select the option Open with from the context menu Select the Choose Program option and choose start_tsm with the Windows batch file icon from the list If this option does not appear in the list choose Browse navigate to the TSM_HOME directory and select the file start_tsm bat from the file list It should only be necessary to do this once Notes 1 If the option Always use the selected program to open this kind of file is checked simply double clicking on the file icon will in future load the file into TSM Only choose this option if you don t edit this type of file in your spreadsheet program by default 2 The directory containing the data
89. e simpler model often provide the best starting values for those parameters 136 James Davidson 2008 in the more general one This stepwise approach to the optimum is often successful when an attempt to optimize the full model from the default initial values ends in failure 5 As a last resort try keeping a parameter away from illegal values by imposing inequality constraints Set them in Values after checking the checkbox for Parameter Bounds 6 The estimation output can be optionally printed in the event of non convergence but note the caution given on the Options Optimization and Run help page regarding the interpretation of these reported values Ja Switching regime models Markov switching and smooth transition models often exhibit multiple maxima of the likelihood Good starting values and careful experimentation with different starting values are strongly recommended As a switching probability tends to 0 or 1 the likelihood becomes flat due to the logistic mapping employed and the algorithm can get stuck at these points Restarting with plausible probability values such as 0 9 0 1 often succeeds in this situation 8 The simulated annealing algorithm uses randomization to decide on successive steps With a multi modal criterion function it is possible if rare for successive runs of the search algorithm to converge to different points Running SA for a limited number of steps before starting BFGS also
90. e Optimization Estimators and restart TSM 15 James Davidson 2008 X XX In the Select Estimator box choose Least Squares Select your dependent variable from the list Use the scroll bars to select the desired AR and MA orders p and q Select a Type 2 intercept this is identified even if you have a unit root You cannot have both types at once so deselect the Type 1 intercept first if necessary Press Go or the Running Man button If your run has been successful you should see Strong Convergence in the results window If you aren t sure what p and q to choose you can have the program try each pair in succession up to a chosen maximum Click Setup Multiple ARMA Models and select the maximum values you want to try Click the Running Man with this dialog open and see the estimates computed successively in the results window You can choose a preferred specification by comparing the Akaike Schwarz or Hannan Quinn selection criteria for each model To estimate an ARIMA p 1 q model check the Impose Unit Root box 9 HOW TO FORECAST WITH AN ARMA ARIMA MODEL x Having selected your model choose Options Forecasting and use the scroll bar to select the number of post sample periods to forecast Note that you cannot forecast beyond the end of the data set if your model contains exogenous variables Select the options Ex ante Multi Step and Analytic Now open the Options Output and Retrieval
91. e a block of highlighted variables with a single command but in this case the highlighting is cleared for all but the last Resize Sample Use this command to create additional space for data to be entered by hand or created by simulation Type the desired number of observations into the text box provided If this number is less that the number of observations already existing the sample is trimmed to the specified length CAUTION Excess observations are deleted this operation is not reversible If the number is greater than the current length existing series are extended with NaN values A new variable Zeros is created automatically with the full number of observations with value 0 Notes 1 Use Zeros as the dependent variable when specifying a model for simulation renamed as required 2 If the data set is initially empty when this command is given give the command File Data Clear to clear the current set the new data set receives the associated file name newdata xls Set Sample Start Trims the number of observations specified from the start of the sample When lags are created additional rows are added to hold the pre sample observations with other variables set to NaN This command can be used to remove these extra rows if desired CAUTION this operation is not reversible Delete Selected Rows This command deletes complete rows from the data matrix for which the the selected variable equals t
92. e border and drag with the mouse BUTTONS 1 The Refresh button rewrites the values field to reflect changes to the model specification Pressing the Values button in the relevant Model dialog has the same effect The Clear button refreshes the fields after setting all values to defaults The Equation and Equilibrium Relation dialogs have buttons for cycling through equations relations An alternative navigation method is to use the choice widget on the tool bar All dialogs except Markov Probabilities and Smooth Transition have a Next Regime button that appears when switching regimes are specified Note that if the parameters in question have not been selected to switch then Regime 1 shows the common values for all regimes and the dialogs for Regime 2 and above are blank All dialogs have a checkbox for selecting parameter bounds and grid plotting This shows hides two columns of text fields for entering bound values see paras 10 14 below Checking unchecking the box in any dialog effects the setting in all the Values dialogs VALUES FIELDS 6 The values attained in an estimation run are displayed in the Values fields to double precision machine accuracy These provide the starting values for a new run and can be edited FIXED PARAMETERS 7 Check Fixed to fix the parameter at the value set during estimation Applications of this feature include Suppressing intermediate lags in ARMA GARCH models fix the
93. e capabilities as the Excel 2 spreadsheets created by Ox and are widely portable Contain graphs and listings associated with the stored model having the same name as the file These are loaded when the model is loaded Their contents can typically be recreated by re running estimations and hence they are treated as temporary They will be deleted when the model is deleted and also at closedown 1f the general option Delete Temporary files on Exit is checked Text files containing Ox source code They can be executable such as tsmod_run ox but can also be included in other ox files using the compiler directive include In normal use a user s code files should be tinclude d in the standard code file usercode ox which is in turn included in the executable tsmod_run ox Graphics file produded by Gnudraw formatted for input to Gnuplot These files are deleted by default after Gnuplot has processed them but are optionally saved in the Results directory for further processing by the user They are ordinary text files and can be viewed and edited in Notepad OxEdit and similar programs The default bitmap graphics format This format is read by a wide range of commercial graphing and word processing software and converted to formats such as bitmap Jpeg Tiff etc Default vector graphics format Can be read by various public domain software and converted to wmf emf and other formats by most graphics packages Ca
94. e equation regression models the regressors except lagged dependent variables are held fixed in repeated samples In cointegration models this is an unrealistic assumption even in large samples It is better to consider a multi equation model in which the unit root processes are generated endogenously Monte Carlo experiments can be used to evaluate inference procedures in this case 11 Directories and Files DIRECTORIES Windows folders Start in Must be specified by the operating system when TSM4 starts This is usually set by the short cut used to start the program Options are presented by the installation program or it can be set manually by editing the short cut Otherwise by default it is the directory where the Ox file used to start the program resides Notes 1 On networks or shared systems the user must have write permissions in the Start in directory Write permissions in the TSM Home directory ox home packages tsmod4 are not required It is NOT recommended to designate TSM Home as the Start in directory 2 In the Windows installation of TSM double clicking on a tsm file in Windows Explorer starts the program with the settings in question The Start in directory is one where the tsm file resides If the file is selected from a Start Menu the Start in is the user s registered home directory Results Selected by the user as an alternate location for program outputs By default it is the same as the Start in
95. e parameterization 85 James Davidson 2008 6 Actions 6 1 Actions Run Estimation Closes all dialogs saves the current configuration in settings tsm and starts estimation of the currently specified model To have the dialog box configuration restored automatically after the run is finished select this option in General Options Alternatively re open by hand with Actions Restore Dialogs Notes 1 This command can also be started with the Run button on the toolbar and with the Go buttons in the Model Linear Regression and Model Dynamic Equation dialogs Za Sequential and iterative calculations can be interrupted while in progress by clicking the Run button on the toolbar A choice box appears possibly after a short delay with the option of aborting the run or continuing BATCH JOBS 3 If the checkbox Run Next Estimation as External Process is checked in Options Optimization and Run before the command is given the run is performed externally by starting a new instance of Ox 4 If the checkbox Defer External Jobs is checked in Options General the Ox file containing the job is created but not run Use this option if the job is to be run on a different machine for example 6 2 Actions Evaluate at Current Values This command is the same as Actions Run Estimation except that the optimization algorithm is not called The post estimation output is simply created at the parameter values curre
96. e second the horizontal axis X Reverse the ordering if desired in Setup Data Transformation and Editing Edit Move Up Move Down If only one variable is highlighted nothing is plotted Other options can be selected at the same time and will be displayed for all highlighted variables 6 In a scatter plot the two regression lines Y on X and X on Y are superimposed by default Note that these both pass through and therefore jointly indicate the point of sample means The more nearly parallel these are the higher the correlation between the variables Unselect this feature in Options Graphics 7 The sample selected for plotting Sample 5 is independent of the samples set concurrently for other program functions See Setup Set Sample for details If data are missing for part of the specified period nothing is plotted for these observations MULTI_SERIES PLOTTING This option allows up to 8 series to be plotted on one graph with line styles selected by the user This option gives the user more control over plotting styles than is available with simple plotting Check the Multi Series Plot Checkbox l Choose a line style 1 8 using the radio buttons and then a variable from the list at most one variable can be selected for each style A Repeat for up to 8 series i Press Go Notes 7 Multiple series plotting only works for time plots Other types of plot are shown in the usual way in separate graphs in a co
97. eated as fixed in the usual way 2 Output to the results window includes the grid location of the criterion maximum and also locations of the largest values of the test statistics including absolute t ratios diagnostic tests and any specified tests This feature can be used to implement tests where parameters are unidentified under the null hypothesis The usual procedure is to base a test on the supremum of the statistic over eligible values of the unidentified parameter s 6 7 Actions Multi Stage GUM This command allows the computation of efficient GMM estimates where the weights matrix is estimated to allow for heteroscedastic or autocorrelated errors This is a two or multi stage procedure performed by issuing this command repeatedly Proceed as follows E Select the covariance formula required Robust or HAC in Options Tests and Diagnostics di Select GMM as the estimator in Setup Estimators and Sample 89 O James Davidson 2008 F Formulate the equation s in Model Dynamic Equation Select the instruments in Model Select Instruments l To compute the first stage estimates equivalent to regular IV GMM give the Actions Multi Stage GMM command To compute the second stage estimates using the first stage estimates to construct the required residuals give the Actions Multi Stage GMM command a second time before any other command To iterate the procedure repeat the last command as often as req
98. eceeceseeecaeceeneecaeeeeaeecaeeeeaeecsaeeeeneees 104 8 2 Options Tests and Diagnostics ceeccecesececseececeeceeceeneeceeeeecseeeeesteeeesaeees 104 Q TESTS FOR SERIAL DEPENDENCE o eee ceecceencecesecesececeaeceeeceeneeeneeceereseneeceeneeeneeees 104 DIAGNOSTIC TESTS iii vce n tacit A E ETA ERA E EE NENE 105 SCORE LM TESTS ariora np A R ETAR EEEa 105 CONDITIONAL MOMENT CM TESTS cocococccononononcnocnnonnnconcnconnncnnnnnonnncnnnncon cacon nconnncnncnnos 106 OTHER DIAGNOSTIC TESTS aeea E E r E EA R A E ERE 106 BOOTSTRAP TEST OF WO mernet io A E AE EREE T LE 107 COVARIANCE MATRIX FORMULAE cc eeccecesecesnceceseceeneecaeeeeneeceaeeeeaeeceaeeeeneeetneseneeens 107 HAC KERNEL FORMULAE AND BANDWIDTH o ooooccoccoccnoccnononcconnnoonnnnonccnnnnncnncccnnnnnnnccnno 108 MODEL SELECTION CRITERIA cher a ri i e RE EER REE EER R ER 108 LM TESTS OF RESTRICTIONS AND FIXED VALUES c cooocococcconononoccconononnncconanonnncnnnnos 108 SUPPLYING AN EDF FILE FOR P VALUES oocccoocccocccconnnconncnonnnonncconononnnocononcnnncconenconncnnes 109 8 3 Opuons Forecastihg eiii ir atole caos 109 FORECAST Suns Roi polilla rr 109 FORECAST TYPE umi idas 110 MULTI STEP FORECAST METHOD reiecta eE E N EAERI 110 MONTE CAREO SETIINGS cups RE AEA AEEA 111 ACTUALS IN FORECAST PLOT eieae E E e chaste batons A E EEA 111 CONFIDENCE BANDS a Ea E E N tena E EA EEAS 112 PLOT DISPLAY cremi E EE E E coh betes E EE E R RRR es 112 IMPUESE RESPONSES orere ne anen R Ea EEE
99. ecting the backup file Note that restoring settings does not reset the run ID counter Named settings files are also useful in a teaching context Students can be supplied with a tsm file containing a desired set of defaults and also stored models for estimation or simulation exercises The students can 138 O James Davidson 2008 18 19 easily undo any changes they have made by reloading the defaults file By default settings files are saved with local path information to locate data and listings files which may make them unsuitable for transfer from one installation to another Use the Export option in File Settings Save As to omit this local information The search path for all files will then be set to the Start in directory when the settings file is loaded For example a class exercise with preset model specifications and data could be distributed by bundling all the relevant files for distribution e g in a zip file and arranging for them to be extracted to the Start in directory of each target TSM installation To over ride the default behaviour of setting the run ID number to zero in a new settings file add the line RUN_ID to your text file of settings before reloading them as described in Appendix E where is your current ID value DOING SIMULATIONS 20 21 22 A star feature of the program is the ability to stochastically simulate any model that it can estimate using either rand
100. ed On occasion Java can fail to display the scrollbars correctly If this happens try closing and re opening the dialog or just drag on the list to scroll it 4 In some cases e g selecting the dependent variable only one list selection 1s allowed at a time In others multiple selections are allowed Clicking a name has a toggle action select when unselected deselect when selected In some dialogs double clicking a list item simultaneously selects the item and launches the appropriate action on it e g displaying a plot 5 To quickly select a block of adjacent names on a list use drag select In other words click the first name then click the last name and drag the mouse briefly with the button held down The dragging action highlights all the names between the two selected cases Deselection of a selected block works the same way click the first highlighted name then drag the last highlighted name A simple way to clear all the selections in the list is to first drag select the whole list then drag deselect it 6 The dialog object most recently clicked on is said to have the focus and is outlined by a broken rectangle If the variable list of any open dialog has the focus clicking the Chart button on the toolbar displays the plot of the highlighted variable s Note The current settings in the Graphics Show Data Graphic dialog control what items are plotted Vy Options may be greyed out disabled i
101. ed from this menu The Model menu is where model specifications are set up The Values menu is for setting starting values and selecting options for model parameters The Actions menu does things Some of these menu items open dialogs but most perform actions directly The Graphics menu is to display graphs An estimation must be run before the equation graphics options are available The Options menu is to change program settings The Help menu gives access to the complete user s manual also available in PDF format and the list of data names and descriptions 1f these have been created It also contains commands to open the Registration dialog and About window Close a dialog by clicking the Close button X on the menu bar Positions on the screen of closed dialogs are remembered even between sessions This allows the user to create a personalized work layout on the desktop Use the Reset Dialogs command to centre all dialog positions Submenus and menu items are greyed out when the command is currently unavailable For example a data file must be loaded before any action apart from changing options is possible Remember that to activate a model option e g Conditional Variances Regime Switching it must be selected in the Model Dynamic Equation dialog Just setting the required options in the dialog does not do this Values dialogs will not reflect a change in the model specification until either 18 O James
102. ed in the Values dialogs 6 12 Other Commands SET DEFAULT VALUES This command sets all free parameter values to defaults Fixed values and all fixes bounds and constraint settings are retained CLEAR VALUES This command has the same effect as pressing the Clear button in all the Values dialogs Parameter values are set to defaults and all fixes except defaults bounds and constraints are removed 93 James Davidson 2008 CLEAR RESULTS WINDOW If the results buffer becomes full and will accept no more text use this command to clear it Note that its contents can first be first saved to a file see File Results Save Selected Text CLOSE ALL DIALOGS This command is given automatically before estimation operations are carried out Current window positions are stored RESTORE DIALOGS Reverses the action of Close All Dialogs Use it after an estimation run and also after starting the program to restore the previous window configuration This action can optionally be made automatic see Options General Options Notes 1 The actions of Close All Dialogs and Restore Dialogs are duplicated by the toolbar Windows button which toggles between them 2 Dialog positions for open dialogs are saved between runs Restore Dialogs or the Windows button restores your dialog configuration at shut down 94 James Davidson 2008 7 Graphics 7 0 Graphics General Information Graphics are displayed in a window
103. ed settings file The extension tsm is added to the file name if not supplied Import Models Adds the model specifications stored in a named tsm file to the current settings Existing models and options are not changed Export Exports settings listings and data to a tsm file Settings as Text gt Display Save Settings Writes all the non default settings as text in TSM script format either to the results window or to a file Save Current Model Writes the non default specifications for the currently loaded model to a file Save System Defaults Writes the current system settings as text Clear Replace all settings with defaults see Options General Information and Defaults for a list Notes 1 Settings are saved automatically to the default file settings tsm before any estimation run and at closedown Therefore there is normally no need to save them manually except to a different named file to store them for subsequent reloading 28 James Davidson 2008 In the Windows installation TSM can be started by double clicking on a settings file This loads the file in question as if loaded by the Open command Note that settings are saved to the default settings tsm as usual Use Save As to update a named file IMPORTING MODELS 3 The Import Models command can be used to combine models from different files and also to copy specifications to other installations without affecting
104. ed to the nearest percentage point Check the Save EDFs checkbox to save tabulations of the empirical 53 James Davidson 2008 22 distribution of test statistics If the t statistics are centred on the true parameter values or otherwise if the null hypothesis of interest is set to be true in the simulation these distributions can be used to provide critical values and hence to estimate true test powers by simulating cases of the alternative These tables can also be used to generate p values for tests in observed data EDFs are saved as spreadsheet or matrix files of the type specified by Options Output and Retrieval Export Listings to Files of Type The assigned file names are of the form EDF_Run run i d extension These files can be renamed merged and or edited either in TSM or a spreadsheet program see below See Appendix G for details of the EDF file format RUNNING AN EXTERNAL PROCESS 23 24 25 26 Check the Run as External Process checkbox to launch the run as a batch job in a console window The calculations are a run in a new instance of Ox running in a console window A temporary executable Ox file is created to be run in batch mode This option allows the TSM GUI to remain under the user s control for other tasks while a long Monte Carlo job is performed It also allows two or more jobs to run be concurrently Since Ox is not multi threaded this is the best way to make full use of a mul
105. eecceececsseceeneecaeceeneeceaceseaeecaeeeeneceseeeeneeceneeeneeees 121 GARCH PARAMETERIZATION ceeccecssecesececeseceeeeeceaeceeeeeceaeeesaeecaeeseaeecaeeeeneeceaeeeeneees 122 OPTIMIZATION SETTINGS cuca da dona Lea dades leia ciedad tic 123 8 7 Options Optimization and RUN cooococcnoccnononcconnccnnnnnncnnnnnnnnnnnononccnnncnnnnnnoss 123 OPTIMAND CONVENTION iodo sskscaaecosse sev assbesecatsestesehessapeontssdass ri a aaah EAEE a EE ERENS 123 NUMBER OF GRID POINTS nci kurre a E R Te AEE A RITES 123 BOUND ON DYNAMIC PARAMETERS 0 ccc ceeccessseesseceeeeeceseceeneecaeceeneecaeeeaeecenneeeneeees 124 OPTIMIZATION SETTINGS BFGS ALGORITHM cece ceeceeneecseeceeeeeceeeeeeeeeceseeeneeees 124 SIMULATED ANNEALING pa era E Ea ETEA ER ETE aS stout EAEE a TERAS 124 NON CONVERGENCE ven aei ia O ERN eea E E r EAREN 124 RUNNING AN EXTERNAL PROCESS 00 oe eeccceeecesceceseceseeecaeeeeceecaeeeneeceeeeeaaeceeeeeeneeens 125 8 8 Options 7 General Options ia 125 OPERATIONAL SETTINGS eie ee aei e e a a ie EN eaa i odres 125 DISPLAY SE TAIN GS a reaa E aae a A E EAE EEEa Nee eNi iE 126 LINEAR REGRESSION MODE eerren eiren a e EA EEEa NAE EEE 127 DEFER EXTERNAL JOBS nee naea a aari a on AAE Ea A aE ARESO 127 ASSIGNABLE TOOLBAR BUTTONS 0 ee eeccecsscceseceseceeeeecssecesececeeeeeeaeceseeeeeeecseeseeeeees 127 A A A een seevaaneiapanedsaueaeeldeeecearoanedts 128 USER S MANUAL 00 ta o tb ri aseo 128 VIEW TEXT FILES aea tna eor cion EES EEE EEEE
106. electing the same set variables as the Dependent Variables and as Regressors of Type 2 with k gt 0 lags selected results in the unrestricted VAR k system being estimated 9 The trend term if selected with the checkbox is a regressor of Type 1 With this option selected lags of Type 1 regressors are disabled to avoid collinearity WALD TEST OF CONSTRAINTS 10 Estimation subject to constraints is not available for linear regressions LM tests of parameter constraints and fixing restrictions are likewise disabled although parameters can be fixed in the usual way However note that Wald and LM tests are equivalent in this case 11 To perform an F test of significance of the regression check the Wald Test checkbox and also the Test Joint Significance of Regressors box in the Model Constraints dialog Note that lagged dependent variables current endogenous variables in simultaneous systems and the trend term are not included in this set by default but can be added to it by checking the Wald Test checkboxes in the values dialog COINTEGRATING REGRESSION 12 The cointegration options are all disabled if the Systems checkbox is checked or the Estimator selection is IV 2SLS The Phillips Perron and ADF statistics are only available with OLS estimation These options are disabled if FMLS or SSW LS are selected 13 The Phillips Perron test and FMLS estimator both make use of a Heteroscedasticity and Autocorrelation Con
107. ell as the styles listed under 7 The default date display mode is selected automatically when a new data set 117 James Davidson 2008 1s loaded Alternative settings must then be re selected in the dialog The defaults are YYYY for annual or quarterly data MM YYYY for monthly and higher frequencies 3 DD MM Y Y for dated daily or weekly data k No Dates for undated data BITMAP DIMENSIONS 9 The dimensions of PNG bitmaps are selected by entering the numbers of column and row pixels desired The default is 640x480 If O is entered in the column row field the setting is automatically calculated as 3 4 times the row value 4 3 times the column value NOTE These settings do not affect the screen display ACTUAL FITTED RESIDUAL PLOTS 10 The Double Chart button on the toolbar displays by default time plots of the actual and fitted values and the residuals The button is disabled until an estimation has been performed If the option Extended Actual Fitted Residual Plots is checked two additional plots are shown the actual fitted scatter plot and the histogram and kernel density of the residuals together with the normal density curve with matching mean and variance for comparison CONFIDENCE BANDS 11 By default multi step forecast plots show 2 standard error confidence bands or 95 estimated confidence bands in the case of Monte Carlo forecasts The following options available for confidence ban
108. elow by zero In some models such as highly persistent FIGARCH models the GARCH intercept can be very small and estimation close to the parameter boundary poses numerical problems These are eased by making the square root or other fractional power the parameter to be estimated The default value which works well in most cases 1s 2 Try raising this to 4 if there is evidence of a problem Set to 1 to estimate the variance intercept directly Be careful to set the starting value and interpret the estimate appropriately The Student s t degrees of freedom d f parameter is bounded below by 2 and is infinite in the Gaussian case A square root transformation the default better numerical performance in the vicinity of these can yield extreme values Setting the order of root to a negative value allows the estimation of the inverse d f which takes the value zero in the Gaussian case Note the variance GARCH intercept and Student t d f parameters are constrained to be nonnegative during optimization by taking the absolute value of the parameter element to evaluate the likelihood function By default the Student skewness parameter is non negative and equal tol in the symmetric case Estimating the logarithm makes 0 the symmetry value and may yield better numerical properties In the default case nonnegativity is enforced as in 3 DYNAMIC MODEL SETTINGS 5 By default up to 10 lags can be set in the ARMA and GARCH models This
109. ented to enter the row offset that is the relative position in the current file of the first observation of the new file The offset is gt zero if start dates match gt positive if start date of new series is later or gt negative if start date of new series is earlier Close the dialog either by pressing Return or clicking the Close symbol on the menu bar Save Saves data under the name specified in the last Open or Save As command Save As Opens the operating system s file dialog for saving The type of file saved options are Excel Lotus123 GiveWin ASCII with load information or matrix file is determined either by the extension or if no extension is added by the current selection in Options Output and Retrieval Options Clear Clears the current data set Tabulations Load EDF File Loads a previously prepared spreadsheet file containing an empirical distribution function This can be displayed in Setup Look Up Probability and Setup Look Up Critical Value and used by the program to generate test p values Files with the correct format are generated by the Monte Carlo module see Setup Monte Carlo Experiment Tabulations Merge EDF File Combines selected file with the resident EDF file When combining tabulations for different sample sizes the names and specifications for the two tests must be identical Tabulations Clear EDF Table Removes table from memory The table is saved with model li
110. erical methods can be disabled and the toolbar buttons hidden For this option uncheck Enable Optimization Estimators A restart is required to implement this selection DEFER EXTERNAL JOBS 15 Check this option to create batch jobs estimations or Monte Carlo jobs as executable Ox files for starting manually Use this option to run the job on a different Ox installation or to defer running it until a convenient time When this option is unchecked the default the job is started immediately the Run command is given ASSIGNABLE TOOLBAR BUTTONS 16 The two toolbar buttons with the Dialog icon and a number can be assigned to open any dialog that does not have a dedicated button Simply open the dialog you wish to assign then click one of the two assignment buttons This also works for the Grid Plot and Simulate commands on the Actions menu Note o Unassigned buttons simply re open the last dialog opened o To remove the current assignment assign a dialog which has its own toolbar button o To assign an Options dialog to a button first uncheck the Automatically Close Options Dialogs checkbox This allows you to open another Options dialog without closing this one o To assign Options General itself to a button press an assignment button before opening any other dialog 127 James Davidson 2008 9 Help x User s Manual gives access to these pages View Text Files opens additional documentation i
111. erted moving average roots diverging to infinity It will not normally need to be changed To remove set it to a large value OPTIMIZATION SETTINGS BFGS ALGORITHM 4 The options Maximum Number of Iterations Iterations Print Frequency Strong Convergence Criterion and Weak Convergence Criterion are set to their Ox defaults with the value 1 They will not normally need to be changed Printing of the current position and gradient is performed every N iterations where N is the print frequency This output is under the control of the Ox routine and will not appear in the TSM results window It goes only to standard output meaning either the console window or OxEdit GiveWin output depending on operating mode Set frequency to 0 for no printing Due to rounding error the efficiency of the search algorithm can be sensitive to large differences in scale between parameters This can be due to inappropriate units of measurement for example Setting the Parameter Rescaling Factor to 1 adjusts parameters to have a similar order of magnitude based on the starting values hence this setting alone will not have any effect with default starting values However setting to a value greater than 1 scales all parameters up to limit rounding error The value of 10 appears to improve the performance of the algorithm in at least some cases However no verified guidelines can be offered Experiment and report your findings please To disable
112. es Simply press Go to execute Any highlights in the variable list are ignored in these cases List Edit Compare Opens a new dialog with a listing of the highlighted series with observation numbers dates e Use the Mark button to compare two series If this command is given for a variable while another is marked the two series are listed side by side To edit an observation either double click it or highlight and press Edit Observation The existing value appears highlighted in the Edit field Type the new value then press o Enter or the Enter key to save the new value move the highlight to the next observation and load this for editing o Copy to save the new value move the highlight to the next observation but retain the new value in the Edit field o Cancel to discard the new value Press Close or the X button to close the editing dialog or Press gt gt gt gt gt or lt lt lt lt lt to list the next previous series in the data set Notes I Use the copy button to repeatedly copy the same value to successive observations for e g easy creation of dummies for sub periods 2 The marked right hand series cannot be edited 3 CAUTION editing cannot be undone 37 James Davidson 2008 Rename After selecting a variable and pressing Go a text field appears for typing the new name The dialog is frozen until OK or the Enter key is pressed to complete the entry If mult
113. escription opens a text field where the description of the selected variable s can be entered Alternatively when the data are prepared for loading in a spreadsheet or text editor add the description text to the variable name normally preceded by a symbol The delimiter symbol can be changed by editing the tsmgui4 h file Some entry formats such as DAT limit the length of a variable name Overflowing text will be lost if the data are saved in this format REGISTRATION T7 The username must be entered in exactly the format as given with the 128 James Davidson 2008 10 unlocking key Changes in e g spelling capitalization embedded spaces etc will cause the registration to fail The program saves the licence file registration txt in one of the two valid locations for this file It first tries the TSM Home directory 1 e ox home packages tsmod4 If either the user does not have permission to write in this folder or if a licence file already exists there it writes to the current Results folder This allows several different licences to coexist on the same workstation if each user maintains a different Results folder By default the Results folder is the start in folder specified in the short cut used to start the program However this location can be changed e g by the command File Results Locate Results Folder and new location is saved in settings tsm If the settings file is subsequently de
114. et up your preferred options for routine operations and use Defaults to store these settings They can then be easily restored by loading this model MODEL DESCRIPTIONS 15 16 17 When the descriptions box is open other dialog functions are disabled However the description displayed can be changed by selecting a different model from the list Use the PgUp and PgDn keys to scan rapidly through the list If the Automatic Descriptions checkbox is checked non default model settings are written to the descriptions box automatically when the model is stored These are coded in the scripting language detailed in the programming manual This provides a convenient way to check that the model specification is as intended Note If either the Semiparametric Long Memory or the Cointegration Analysis dialogs are open when the Store command is given the settings written relate to those modules otherwise the usual model settings are written If the Print Descriptions checkbox is checked the model description if any 44 James Davidson 2008 is written to the results windows when the model is loaded DELETING MODELS 18 When a model is deleted the associated tsd file is deleted from the disk Also note that these files are overwritten when a new model is stored with the same name 19 There is an option to remove all the tsd files automatically at shutdown Their contents except for Monte Carlo results can be regene
115. f they are not compatible with other selected options For example GARCH and Markov switching options are not available unless a maximum likelihood estimator is selected In some cases a reminder message is displayed if an illegal selection is attempted 8 Make a selection with a horizontal scrollbar by dragging the slider or by clicking the arrow buttons at each end for step by step selection Some scrollbars e g for numbers of Monte Carlo replications are incremented in jumps 10s 100s depending on the range of the selection 1 5 Entering Formulae Algebraic formulae can be submitted to the program in three contexts A Data transformation B Nonlinear parameter constraints C Nonlinear equations for estimation or simulation including equilibrium relations nonlinear MA terms and nonlinear ECMs Formulae are typed into a text box which is opened by the following commands Case A Setup Data Transformation and Editing Edit Make Formula Case B Model Constraints Enter Code select Coded Restrictions Case C Model Coded Function TYPING FORMULAE The general syntax is of the form name formula 22 O James Davidson 2008 Case A name is a new variable name Case B name is an existing parameter name Case C Equation name is optional must match selected dependent variable s in Dynamic Equation dialog Case C Residuals Omit name and formula implicit A formula can be constructed
116. fferences of the measured variables See the main document for details 13 Check the third checkbox to parameterize the fractional integration parameters for Equations 2 as the differences from the corresponding parameters in Equation 1 This option allows the restriction of equal fractional integration parameters across equations to be easily tested and imposed in the usual way by setting the Fixed checkboxes in the values dialogs NOTE It is not necessary to specify a fractional VECM to set this option It applies also to a regularly cointegrating or non cointegrating VARFIMA model and also to the fractional lag parameters of a system FIGARCH or HYGARCH specification 14 If Impose Unit Root is specified in Model Dynamic Equation the VECM is estimated with unit roots imposed in the short run dynamics while the Eq R s enter as lagged levels 4 8 Model Select Instruments This dialog is enabled only if IV GMM is the selected estimator Highlight by clicking with the mouse those variables to be included as instruments Use the checkboxes to indicate whether the intercept and trend dummies and lagged endogenous variables are to be used as instruments The Clear button unselects all variables Notes 1 Any variable appearing in the equation but not in the instrument list is treated as endogenous 2 Any variable appearing in the instrument list but not in the equation is an additional instrument Lags of addition
117. fore larger values are preferred This convention can be optionally reversed see Report Minimand in Options Optimization and Run R Squared is the squared correlation coefficient between the dependent variable Y and the model predictions actual Y residuals Therefore 131 James Davidson 2008 15 16 1t is well defined for any model and must lie in 0 1 However whether it 1s a useful measure of model performance depends on the model it is of no use in assessing GARCH models for example R Bar Squared is calculated as 1 1 R squared T 1 T p where p is the number of parameters fitted in the model When models are estimated by Instrumental Variables from the Linear Regression menu the Sargan and DWH Durbin Wu Hausman statistics are given These are asymptotic chi squared statistics under HO with degrees of freedom indicated and nominal p values shown in braces The Sargan statistic is N times the ratio of the GMM minimand to the residual sum of squares where N is sample size This tests validity of over identifying restrictions The DWH statistic tests for valid exogeneity assumptions on the instruments and is N RSSO RSS1 RSS1 where RSSO is the sum of squares from the OLS regression and RSS1 the sum of squares from the regression including the reduced form residuals for the included endogenous variables CONVERGENCE ISSUES 17 18 All estimations specified in the Model Dynamic Equati
118. graphs DATED OBSERVATIONS 12 13 14 15 To set individual daily dates create the data set in Microsoft Excel Enter the dates in column A of the file in Excel date format yyyy mm dd If present these dates will be used by TSM to label the observations This is the preferred method of dating weekly and daily data since the irregularities noted in 11 are taken care of Note You must use Excel or equivalent software to create the dates This cannot be done in TSM If dated files are merged in TSM the dating information in both files is ignored Use Excel or equivalent software to perform merging operations before loading Dating information is used automatically if it is present To over ride this behaviour and set periodic dates in the default manner use the Set Dates command in Setup Date Transformation and Editing Edit In this case the existing date information is deleted When dated observations are saved in Excel format column A of the spreadsheet contains the usual Ox default dating information The column of dates is created as column B with the heading Date in row 1 The first column is ignored when TSM reloads the file and can be deleted from the spreadsheet if desired 33 James Davidson 2008 2 3 File Results Results and information appear in the program s text window The output can be saved to disk files in two ways 1 Select part or all of the window s contents using the mouse a
119. h new step See the Setup Recursive Rolling Estimation dialog for details of setting up the run The sequence of results for each sample period can be exported to a file according to the setting in Options Output and Retrieval Options or viewed as graphics The items available are the parameter estimates with 2 standard error bands plus optionally regression statistics including criterion values residual moments autocorrelation tests stability ex post forecast tests and also any tests of parameter restrictions that have been set up Notes 1 The sequential model selection criteria are not recorded These would differ from the estimation criterion by the same fixed amount in each run so the latter contains all the relevant information 2 If N step ahead ex ante forecasting is specified see Options Forecasting and Simulation the Nth forecast step and standard error or percentiles for Monte Carlo forecasting are reported in the output By default N is fixed so that the actual date forecast moves forward with the sample There is an option to keep the terminal forecast date fixed so that N contracts as the end of the sample advances See Setup Recursive Rolling Estimation for details 3 This command is launched by the Run button on the toolbar if the Setup Recursive Rolling Estimation dialog is open 4 On checking the Report Convergence Status box a sequence of symbols is printed in the results window to sh
120. has the effect of randomizing the BFGS starting value Repeating a run from different starting points or with different algorithm settings is always a good idea While a preliminary SA search is the default setting it may be preferable to have SA switched off as the default and enable it only when needed This will certainly speed things up CHOICE OF SYSTEM ESTIMATORS 9 Don t overlook the distinction between the Linear Regression and Dynamic Equation options The latter always uses numerical optimization to compute the estimator even when a closed form solution exists Large unrestricted VARs may be computed in the Linear Regression dialog using SUR Exclusion restrictions can be imposed by fixing parameters although they can be tested only by Wald tests on the unrestricted model 10 There are two ways to estimate a Gaussian linear equation system by maximum likelihood Least generalized variance LGV optimizes the concentrated log likelihood function the log determinant of the covariance matrix The Gaussian ML option estimates the log likelihood as a function of all parameters including the variance matrix and hence is much more computationally intensive than LGV This method is only required for models with nonlinear features such as ARCH GARCH or Markov switching USING THE RESULTS WINDOW AS A TEXT EDITOR 11 Text can be typed or pasted freely into the window To paste from the clipboard right click in the text area and ch
121. he Model Dynamic Equation dialog The regressor radio buttons are highlighted lighter grey to show a selection has been made Clear all specifications with the Clear button If the GARCH radio button is selected the Asymmetry checkbox selects the Threshold GARCH GJR model In the other cases the signed terms of the APARCH or EGARCH are included suppressed depending on the setting of this checkbox The dependent variable s in the equation s can be chosen as GARCH regressors of Type 2 provided the lag length is set to 1 or greater In this case the zero order lag is suppressed and the lagged dependent variable s act as GARCH regressors This is similar to the option in the mean model Dependent variables are NOT permitted as regressors of Types 1 or 3 These options are cancelled automatically If the Abs checkbox is checked the output shows the variable names enclosed in It is recommended to check this option when lagged dependent variables are selected especially when running simulations The Garch M panel allows either the conditional variance or conditional standard deviation to be added to the regressors selected in Equation Choose the regressor Type and Mode using the radio buttons MULTIVARIATE GARCH 8 If the equation system option is selected the default is to have fixed correlations between the variance adjusted residuals An alternative is the DCC model in which the elements of the cor
122. he Model Equilibrium Relations dialog Presample lags are replaced by 0 For the Equation option an equation code must pair with a selected dependent variable see the field heading It is not possible to add an equation without first selecting a variable Equations can be validly entered in the explicit format Dependent Variable Formula The name of the dependent variable is added implicitly if omitted In the Residuals option the dependent variables must still be selected even though there is no explicit normalization The number of equations formulated must be equal the number of selected variables Checking that the formulated equations have a solution for the chosen 69 James Davidson 2008 variables is the responsibility of the user 3 For the Residuals option the typed equations define the model to be estimated Dependent variable selections in Model Dynamic Equation are ignored Be sure to delete any unwanted equations using Clear 4 When System is checked in Models Dynamic Equation and two or more endogenous variables are selected coded specifications can be created for each equation Switch between these with the Next and Previous buttons If no function is specified for a variable enter 0 in the corresponding field NOTE Simultaneity is not allowed E Equation specifications should contain ONLY exogenous or lagged endogenous variables on the right hand side Residual specifications
123. he constant entered in the box The constant value can be NaN to delete all rows where the selected variable is missing E g to extract the observations for a particular quarter from a quarterly data set create seasonal dummies and delete the cases where the dummy for the chosen quarter is 0 CAUTION this operation is not reversible Be careful to save the 39 James Davidson 2008 reduced data set under a new name Make Zeros Make Intercept Make Trend These commands create dummy variables Intercept has values 1 Trend has values 1 2 3 T for a sample of T observations Notes 1 To create an event dummy first create Zeros then edit it observation by observation in List Edit Compare 2 Use the built in intercept and trend dummies for estimation wherever possible Make Normal 0 1 Make Student t df Uses the built in random number generator to create series of independent observations with the specified distribution Make PDL Creates polynomial distributed lag variates see main document for details for highlighted variable s with lag length specified by the scroll bar Five new variables are created corresponding to terms of order 0 up to 4 in the lag polynomial Delete any unneeded cases Reverse Data Operates on the whole data set listing the observations in reverse order Sort Data By Operates on the whole data set sorting the observations according to the ascending order of the hig
124. he number of extra observations added at each step Set by dragging the scrollbar Setting this equal to 1 may be excessively slow to execute If it is set greater than 1 the sequences of estimates are plotted as step functions The terminal observation required will in most cases be the maximum available This scrollbar allows it to be set smaller Note that the lower limit is constrained by the initial sample and step size settings The first check box allows the option of saving regression diagnostics and test statistics to be selected This is on by default The second check box allows saving to a file of all the forecasts for each estimation period NOTE The forecasts other than the N step ahead cannot be displayed interactively The Go button duplicates the Actions Recursive Rolling estimation button If this dialog is open the Run button on the toolbar is a third way to launch the run A confirmation box opens to guard against accidental launches By default the number of forecast steps N is fixed and the N step forecast is reported for each recursion step If the second check box is checked the terminal forecast date is fixed so that N contracts as the end of the sample advances This option can be used to compare the forecasts of a particular date from different standpoints 46 James Davidson 2008 3 6 Setup Compute Summary Statistics This dialog presents the variable list Select a variable and press Go t
125. he variable transition probabilities can be plotted For smooth transition models the transition function can be plotted 4 Forecasts and solved MA weights can be computed for the equation and the conditional variance where this is estimated 5 The interpretation of ex ante forecast time plots depends on the forecasting method With analytic forecasting the plots show the estimated mean forecast with optional 2 standard error bands Standard errors are not available for bilinear models and user supplied dynamic models nor for conditional variance forecasts in GARCH models 6 Monte Carlo forecasting generates the distribution of stochastic simulations and the plots show the median forecast and the 2 5 and 97 5 percentiles These therefore define a true 95 confidence band regardless of the error distribution and are available for all models and for conditional variances Kernel density plots of the empirical forecast distributions are also available for any point in the forecast period selected in Options Forecast and Simulation Options 7 To change the type or number of forecasts make the desired selection in the Options Forecast and Simulation dialog then recompute the model using either Actions Run Estimation or Actions Evaluate at Current Values to avoid re estimating 8 To view a plot of the recursive rolling estimations either double click a parameter statistic in the list or select it and press Go The ro
126. here the coded function represents the complete model 67 James Davidson 2008 Then all other model features need to be disabled In particular make sure that items such as the built in intercept are deselected to avoid duplication and an unidentified model METHODS There are three ways to code a model for estimation I Type coded formulae for equations or equation components into the text box interactively IL Supply the code for the model equations as an Ox function and compile this with the program MI Write Ox code as in II but for the complete likelihood function Method I is easiest to implement but limits the function to a single line of code Methods II and III allow any degree of generality but require a minimum of programming expertise Since the function is compiled with the program TSM must be stopped and restarted to make changes to the specification INTERACTIVE CODING To set up the model do as follows 1 Open the Model Coded Equations dialog and select one of the radio buttons Equation Residual Nonlinear MA and Nonlinear ECM 2 Select the dependent variable s in the usual way in the Model Dynamic Equation dialog 3 Type the equation formulae in the text fields Use Previous and Next to navigate the fields Clear to initialize the formula and Cancel to discard changes and revert to the stored text 4 Press Test to check the model parses OK and list the parameter names i
127. hesis is true Note that the upper tail is tabulated so be sure the parameters are signed appropriately 52 James Davidson 2008 15 16 17 18 19 20 21 When the models match the t statistics can optionally be centred on the true parameter values specified by the DGM With this option selected the distributions of the test statistics can be studied under the true null hypotheses that the parameters takes their DGM values This option is available only in those cases where the bias and RMSE are available When the distribution of test statistics follows the distribution specified for the null hypothesis the p values should be uniformly distributed so that their c d f is the 45 degree line of the unit square The Kolmogorov Smirnov statistic the maximum absolute difference between the p value EDF and the uniform distribution can optionally be calculated This provides an alternative to the quantiles to assess how closely the distributions match Nominal critical values for the K S distribution assuming 80 bins are 1 22 10 1 35 5 1 63 1 Note this option is only available if the frequency table is enabled see 19 below If GMM is simulated there are two options available the one step estimator and the efficient GMM estimator using the first round estimates to compute the weight matrix Check the iterated GMM checkbox to select the latter option Further iterations are not possible in th
128. hether the model dynamics are compatible with sample averages adequately approximating their asymptotic distributions in the selected sample size 10 The I 0 test is for single equation models only and is properly intended for use with univariate time series models If the equation contains exogenous variables these are held conditionally fixed in the simulations If they are nonstationary this will in general yield a case of the alternative hypothesis 11 Choose a number of replications large enough to validate the asymptotic tables from Smirnov 1948 say 500 Set the number of replications in Options Simulation and Resampling after checking the Inference by Resampling checkbox to activate the replications scrollbar NOTE This checkbox does not activate the test itself It can be unchecked again after the setting is made 6 9 Actions Compute Forecasts This command generates and displays forecasts after a model has been estimated Note that if forecasts are specified prior to an estimation run they are computed automatically following the run This option allows additional results to be generated Note The command Evaluate at Current Values Calculator button is another way to compute specified forecasts in addition to any specified tests The complete output for the run is printed in the results window in this case This command does not produce any additional output and displays the forecast plots automatically
129. hlighted lighter grey To see the actual variable s selected highlighted in the variable list click on the radio button in question Only one variable can be selected as dependent unless the Systems of Equations box is checked Multiple selection is allowed in the regressor 62 O James Davidson 2008 10 11 categories The Lags setting allows different orders of lag for the regressors of each Type For example include variables for lagging in the Type 2 category and non lagged variables such as dummies in the Type 1 category Individual lags can be suppressed by fixing the coefficients at zero in the Values dialog If neither lags nor ARMA components are selected and there are no current endogenous variables the regressor Types are all treated equivalently If the dependent variable is selected as a regressor of Type 2 and Lags gt 0 only the lagged values are included This provides an alternative way from setting AR Order gt 0 of including the lagged dependent variable as a regressor This feature is for compatibility with the Linear Regression option LINEAR REGRESSION 12 13 14 A linear equation can also be specified in the Model Linear Regression dialog and in that case will be estimated by the usual analytic formulae Models specified in this dialog are always estimated numerically This dialog and the Linear Regression dialog cannot both be open at once One is disabled whenever the other is o
130. hlighted variable Don t select more than one If two or more are selected only the last choice is effective Undo Sort Reverses the action of the Reverse Data and Sort Data By commands restoring the data set to its original order Shape Re assembles by rows a data series of length T into c columns of length ceil T c where c gt 1 is selectable In case T is not divisible by c the columns are padded to equal length with zeros and then with NaNs to fill the rest of the data matrix Uses for Shape include the following 1 Separate the real and imaginary components of a discrete Fourier transform Set c 2 Note the jth periodogram point for j 1 T 2 is the sum of squares of the jth row elements of these columns Ze Separate seasonal data into its seasonal components For example with quarterly data set c 4 If the first observation is from Quarter 1 then the first column created will contain the Quarter 1 observations the second column the Quarter 2 observations and so on TRANSFORM COMMANDS Most commands in this menu can also be executed using the Edit Make 40 James Davidson 2008 Formula command Here they can be perfomed with a single click on any number of highlighted variables Created series is are added to the end of the list with a self explanatory prefix or suffix appended to the name s Use Edit Rename to change the automatically created name if desired Use Edit Delete
131. iately restart it These are convenient shortcuts for loading user s code Windows only Restart Load User Code A choicebox gives the options of loading the currently specified user Ox code and selecting a different code file in the file dialog Restart Load Text Input A choicebox gives the option of selecting a text file containing a set of TSM text commands for loading as program settings and or model specifications Restart Load Text Defaults Loads default settings which if different from the programmed defaults will be set with the File Settings Clear All command and also if the settings file is renewed Restart Simple Restart The system is restarted without changing load options Quit Closes the program The prompts to save specification and data before closing can be optionally switched off go to Options General 26 O James Davidson 2008 Notes Selected text can be cut copied or deleted After highlighting click the right mouse button and select from the context menu The contents of the Windows clipboard can be pasted into the results window at the cursor position Right click with the mouse and select Paste MRU LISTS 3 Commands for loading saving and exporting settings and data files open a popup menu listing the most recently used MRU files The leading item File Dialog opens the operating system s file dialog for selecting other files If a list is empty the popup menu is s
132. if you know what you are doing 8 The specification of the relations can be different when there are two or more of them They nominally contain the same parameters but these can be automatically fixed at 0 if not included in a particular relation See Model Coded Functions for details They can also be restricted in the The Values Equilibrium Relations dialog if desired All Options 9 Eq R s are only included in the model if this feature is selected in Model Dynamic Equation 78 James Davidson 2008 10 The radio buttons in the Types of ECM area allow selection of nonlinear response mechanisms as well as the usual Linear case See the main document for details Three popular variants are pre coded Use the Model Coded Function dialog to define other cases 11 Check the first checkbox in the Fractional Cointegration area to implement a fractional cointegration F VECM model Note that this option is ignored unless the VARFIMA Fractional VECM box is checked in the Dynamic Equation System dialog In this case setting the Impose Unit Root option causes the estimated value s of d1 to be smaller by 1 than otherwise This is taken into account in the calculation of the cointegration order s d3 such that the equilibrium relations appear differenced to order 1 d1 d3 in the system 12 Check the second checkbox to select the generalized cointegration model In this case the cointegrating variables may be fractional di
133. imated by numerical optimization whether or not their form is linear When this dialog is opened the Dynamic Equation Conditional Variance Supplied Function and Regime Switching dialogs are all closed automatically These features are all disabled greyed out until it is closed again All estimators except Least Squares and IV are also unavailable See Model Select Instruments for details of the instrument selection procedure 58 James Davidson 2008 4 Use the Clear button to remove all selections VARIABLE AND LAG SPECIFICATION 5 When one or more variables are selected in any category the corresponding radio button is highlighted lighter grey To see the actual variable s highlighted in the variable list and the lag order selected click on the radio button in question 6 Regressors of Type 1 can have a different lag order specified from those of Type 2 It is recommended to e g make variables for lagging of Type 2 and others such as dummies of Type 1 If lags are not specified then regressors of Types 1 and 2 are equivalent 7 In single equation mode if the dependent variable is selected as a regressor of Type 2 and Lags gt 0 only its lagged value s are included in the set This provides an alternative way to estimate an autoregression without numerical optimization In all other cases as a regressor of Type 1 or with Lags 0 the dependent variable is ignored 8 In Equations System mode s
134. innccnno 138 DOING SIMULATIONS reete ar e ee eE dida 139 STARTING TSM FROM WINDOWS EXPLORER o0oococoocccocccconcnooncononcnconoconenonnnccononinnnccnnes 140 RUNNING SEVERAL INSTANCES OF TSM uo ceeccecesecesneeceeecesceceseeeeneeceeeeeneecenneseneeess 141 TROUBLESHOOTING simios intenet apre DAS 141 5 O James Davidson 2008 What s New TSM 4 25 E Bootstrap test of I 0 eN RGB scatter plots with observation dates colour coded Improved Monte Carlo output format and EDF handling NOTE further revision of EDF file format New data editing transformation options Improved sample selection options Consolidates a large number of small modifications and fixes TSM 4 24 Improved facilities for running and sharing Ox code Code files now bundled with exported settings and viewable from the Help menu x EDF files for tabulations of different sample sized can now be merged p values are generated by interpolating the tabulations according to actual sample size NOTE EDF file and Ox function formats are changed in 4 24 Files created with and for previous versions of TSM must be modified a External batch processing option for estimation and Monte Carlo runs allows multi tasking and avoids tying up the GUI for long jobs Improved plotting controls legends and boxes TSM 4 23 6 Plug in bandwidth selection and pre whitening for HAC covariance estimation New graphics options including forecast fan charts selectabl
135. io buttons allow selection of location of the test variables either the Conditional Mean model Equation 1 included as variables of Types 1 2 or 3 or the Conditional Variance model Equations 2 3 included as variables of Types 1 2 or 3 4 If the selected Type is assigned to include one or more lags see Model Dynamic Equation or Model Linear Regression and Model Conditional Variance then the same number of lags of the test variable s are included in the test set It is not necessary for the null estimated model to contain lags Just set the number of lags required for the relevant Type with the Lags scrollbar in Model Conditional Mean or Model Conditional Variance The degrees of freedom of the test are number of test variables x 1 number of lags Select the F form of the test with the checkbox De There are two ways to run the test Pressing Go will execute 1t immediately using the currently stored parameter values Otherwise the test will be performed following the next estimation run To cancel the test press Clear MOMENT M or CM TEST 6 This options opens a dialog to allow specification of a moment test of the correlation of variables selected from the data set with either T the model residuals or the squared model residuals T7 If the Conditional Moment Test option is selected the joint covariance matrix of scores and moments is computed using the Robust formula see Options Tests an
136. ion This dialog sets the parameters specified for an equation including specifications set in either the Linear Equation dialog or the Dynamic Equation Conditional Variance Supplied Function dialogs Notes 1 The Parameter Bounds Grid Plotting checkbox affects all the Values dialogs After changing the setting press Refresh to display hide the text fields for entry of parameter bounds In multi equation models use the either the Next Equation button to cycle through the equations or the Equation choice widget on the tool bar to switch directly In regime switching models use the Next Regime or the Regime choice widget similarly to see the different regimes If a BEKK multivariate GARCH model is specified the ith columns of the matrices A_j and B_j are displayed in the dialog for equation 1 as Alphaj i k and Betaj i k for k 1 number of equations Be careful to note how these matrices enter the model see the main document for details Although entered and reported in the same style these matrices are not comparable with the multivariate GARCH specification Be careful to interpret them correctly DCC dynamic parameters are displayed in the Values Distribution dialog 83 James Davidson 2008 5 2 Values Equilibrium Relations This dialog shows parameters of the equilibrium relation s Note l If more than one relation is specified use either the Next Relation button in
137. ion and Editing In case C Model Dynamic Equation 5 An alternative to typing a parameter name in full is to type a i or p i or mn A i or P i all forms are equivalent where i is the parameter number Parameter numbers are shown in the Values Equation dialog s 6 The characters 0 must NOT appear in names of variables or parameters Any other characters in particular spaces are ignored Use 23 O James Davidson 2008 spaces optionally to improve readability WARNING Variable names generated automatically in Setup Data Transformation and Editing may contain illegal characters Rename such variables before including in a formula ds The sign to denote multiplication is mandatory Omitting it will cause a syntax error 8 Numeric constants can contain the symbols 0123456789 The symbol decimal point may appear ONLY as part of a numeric constant An isolated is parsed as the number 0 9 Constants are nonnegative A leading minus in any formula is parsed as a unary operator and changes the sign of the operand 10 Definitions of special functions sgn x 1 if x lt 0 1 otherwise pos x x if x gt 0 0 otherwise neg x x if x lt 0 0 otherwise int x integer nearest to x flr x largest integer not exceeding x Indicators ips x 1 if x gt 0 O otherwise ing x 1 if x lt 0 0 otherwise 1z0 x 1 if x 0 O otherwise These functions are not differentiable s
138. ion has been defined a function can still be selected by typing its name into the field The test statistic option from UserTest accessed by checking the Test checkbox is compatible with any estimated model This includes linear equations and the Ox Residuals and Log likelihood options but not Statistic or Data Generation If a coded test is the only programmed option select Test Only and do NOT check the Coded Function checkbox in Model Dynamic Equation If Coded Equilibrium Relations is selected in Model Equilibrium Relations and Equilibrium Relations is checked in Model Dynamic Equation the Coded Function checkbox in in Model Dynamic Equation is disabled Note that in this case the parameter values for the coded relations are displayed in Values Equilibrium Relations For all options except the coded test and coded equilibrium relations the Coded Functions checkbox must be checked in Model Dynamic Equation to activate the option Enter names of parameters in the text fields provided in the dialog Optionally an identifying name can be entered in the Function Name field This is used to identify the output and can also select the function from a code library maintained in the run file Alternatively a name can be passed from the function itself To activate this option leave the Function Name field blank When residuals or the log likelihood are returned setting dependent variable s in the Model
139. iple variables are highlighted each is presented for renaming in turn Delete A confirmation box appears Press the All Selected button to delete all highlighted variables at once otherwise each is presented in turn for confirmation CAUTION This command cannot be undone Description Allows the optional description s of the variable s to be created or edited View these descriptions in Help Data Descriptions Set Dates Allows the dates of observations to be set or changed This works exactly like the method for inserting date information into a data file prior to loading see File Data for details A new column of the data set is created with name ISTARTDATE and opened for editing Enter the initial year in the first row the initial sub period in the second row and the sub period frequency in the third row Enter 2 for half years 4 for quarters 12 for months etc Notes 1 The new column is deleted immediately after the new information is processed 2 The date information is saved with the data in GiveWin or other spreadsheet formats and also in dat files although not in matrix mat files 3 CAUTION This operation is not reversible If the observations are already dated the existing date information will be lost including individual daily dates 4 If the period is set to O the series is treated as undated Observations are numbered from 1 Save Selected Allows a subset of the variables to
140. is release Check the box to do a simulation on log periodogram regression In this case choose the desired options and variable for study in the Setup Log Periodogram Regression dialog before storing the model for estimation The other settings are of course ignored in this case Note that the DGM may either specify a long memory model or another model e g a switching model for an investigation of spurious long memory Note Although the DGM may feature a true d ARFIMA parameter the bias RMSE option cannot be selected since the models assumed are not comparable The bias and RMSE can of course be hand computed from the information reported By default the individual replications are stored These can be plotted as kernel densities or histograms see Graphics menu or written out to a spreadsheet file for further analysis using Files Listings Save MonteCarlo Replications However when very large simulations are run this option may put pressure on available memory Checking the option Save Frequency Table results in the frequencies being accumulated during the run The actual replications are discarded so there is no memory constraint A different routine is used to generate the frequency plots in this case Increasing the number of bins used to generate the frequency distributions gives more accurate estimates of quantiles and test sizes at the cost of greater computing time The default setting of 100 gives sizes estimat
141. is user selectable Initially it is set to the default value displayed as 1 on the scrollbar Move the scrollbar to change the ratio of the bandwidth to the default then redisplay the plot to see the effect The chosen value is stored with the distribution data and used the next time the distribution is plotted as shown by the scrollbar 3 If the scrollbar setting is changed by the user the new value is used for the next plot and replaces the stored value s for the distribution s plotted Tip to avoid changing a stored bandwidth after moving the scrollbar close and re open the dialog before giving the Plot command 4 Monte Carlo graphics are stored in the TSD file created with the Data Generation Model If the TSD file is present reloading this model makes the results and plots of the last experiment performed with this model available to view just as when the model was run To save these outputs store the DGM under a different name before using it for a new experiment 5 The distributions from a simulation run can be stored in an EDF file to supply critical values for tests The currently stored bandwidths for each distribution are used to compute the EDF kernel densities Note EDF file creation can also be done automatically using the default bandwidth by setting the requisite option in Setup Monte Carlo Experiment The present option can be used to fine tune the bandwidths used for each distribution if required 6
142. isabled unless code is loaded and the Test Only option is selected in Model Coded Function In the case where other Ox code is being compiled this test option should be controlled from the same dialog The KPSS RS and HML tests are alternative tests that the residuals are I 0 These are also available for data series from the Setup Summary Statistics dialog and may be useful in conjunction with the ADF and PP tests in the context of cointegrating regression For the truncation parameter c and bandwidth parameter L use the default values or see Harris et al 2006 for guidance BOOTSTRAP TEST OF I 0 19 Check this checkbox to run the test following an estimation run This test can also launched from the Actions Compute Test Statistics menu For further details see Section 6 8 of the Users s Manual NOTE Bootstrap inference for the equation itself is disabled if this option is selected COVARIANCE MATRIX FORMULAE 20 pA 22 Four methods of calculation are available for computing covariance matrices Standard corresponds to the information matrix in ML estimators and is generally appropriate for correctly specified models with iid errors si Robust allows for mis specified likelihoods and heteroscedastic but independent errors X HAC is for models with residual autocorrelation as well as possible heteroscedasticity KVB selects the inconsistent estimator proposed by Kiefer Vogelsang and
143. itional Variances Regime Probabilities a Correlograms and Q Statistics for Residuals and Squared Residuals ES Solved moving average coefficients Forecasts ds Recursive estimation outputs Recursive forecasts Criterion plots Notes 1 Only results for the most recent estimation run can be saved Be sure to save desired outputs before launching another run 2 Files are named uniquely with a descriptive title and the run ID number They are saved to the currently selected results folder 3 Available file formats are the same as for data and are selected in When saving in MAT format the columns headings are listed in the results window 4 There is an option to save all listings automatically see Options Output and Retrieval 2 5 File Graphics Saves the most recently displayed graphic to a file Notes 1 File types and bitmap dimensions PNG files are selected in Options 2 Graphics There is an option to save all graphics automatically as they are displayed see Options Graphics 35 James Davidson 2008 3 Setup 3 1 Setup Set Sample Select the sample for estimation and other data analysis procedures using the scrollbars Date information is given if provided with the data The maximum sample is selected by default Notes 1 The sample is automatically truncated to exclude missing values of any variable in the model specified Remember that missing values are created by taking lags le
144. ive the one off simulations Monte Carlo experiments and bootstrap tests See the main documentation for details and formulae Model uses the distribution specified by the likelihood function if a maximum likelihood estimator is specified If the estimator specified is not ML then Gaussian shocks are used with variance equal to the residual variance from the last estimation Gaussian uses normal random numbers with zero mean and the variance specified in the text field provided Bootstrap Block Bootstrap randomly resamples the actual residuals 112 James Davidson 2008 with replacement The resampled series is centred and multiplied by a bias correction factor of sample size degrees of freedom 1 e n n k The block bootstrap is implemented by choosing a block length gt 1 Sieve AR Bootstrap an alternative to the block bootstrap for dependent data whitens the residuals before resampling Wild Bootstrap preserves the heteroscedasticity of the original sample Instead of randomly resampling the data are randomly transformed by a drawing from a two point discrete distribution X The wild bootstrap and sieve AR methods can be combined for dependent heteroscedastic samples The Fourier bootstrap resamples from the discrete Fourier transform of the residuals using the Rademacher wild bootstrap and returns the inverse transform of the resampled series An alternative to the sieve AR suitable for Gau
145. kipped and the file dialog opens directly The maximum number of files on the MRU lists is an installation option see Appendix B The default setting is 5 MRU lists are stored in the settings file When settings are loaded the current lists are appended to the new ones as space permits RESTART T 10 The Restart Load User Code command causes the file usercode ox to be created if necessary then edited to contain the line include chosen file The chosen file must have extension ox If necessary the executable Ox file tsmod_run ox is also edited to include and define USER_CODE include usercode ox compiler directives Note Only one code file at a time can be compiled Any other include statements are deleted from usercode ox Other lines are commented out The Restart Load Text Input command causes tsmod_run ox to be edited to include the directive define TEXT_INPUT and the statement Text_Input include chosen file which include the contents of the chosen text file as lines in the Text_Input function After the restart these lines are deleted to restore tsmod_run ox to its previous state The Restart Load Text Defaults option edits tsmod_run ox with permanent effect To restore the standard default settings edit the file and comment out the define TEXT_DEFAULTS line The defaults file can also be modified in a text editor See the programming manual for information on text
146. l curve with matching mean and variance can be optionally superimposed for comparison see Options Graphics 54 James Davidson 2008 29 See 7 3 Graphics Monte Carlo Graphics for further information about creating plots including the ability to combine density plots from different experiments for comparison 3 11 Setup Tail Probabilities and Critical Values This dialog gives access to tabulations and plots of standard distributions the standard normal and Student t either signed or absolute and the chi squared and F distributions x Notes Select the radio button for the distribution required Set degrees of freedom as appropriate except for EDF from File see Note 4 below Depending on the dialog opened enter either the critical value to get the tail probability or the tail probability to get the critical value To show the probability critical value also printed in the results window press the right hand button To plot the density with the tail area shaded press the left hand button The tail probability is the area of the upper tail of the density to the right of the critical value Use the critical value to perform a 1 tailed test with the corresponding significance level The distributions INormall and Student tl allow calculation of p values for 2 tailed tests These correspond to the p values reported with the estimation output Use the signed distributions Normal and Student t
147. late p values by interpolation For example suppose tabulations for T 50 100 200 and 500 observations have been created and merged If the actual T is 150 a weighted average of the tabulated p values is returned with weight w 200 150 200 100 42 0 25 on the case T 100 and 1 w 0 64 on the case T 200 i e greater weight on the larger sample size than with a linear interpolation If T exceeds the largest tabulated sample size or is less than the smallest then the nearest values are used with weight 1 8 3 Options Forecasting FORECASTS 1 The levels forecasts include 2 standard error bands These are asymptotic and do not allow for parameter uncertainty For conditional heteroscedasticity models they are computed dynamically using the volatility forecasts The scroll bar label shows the number of forecast steps selected The date or observation number of the final step which depends on the sample selection see Setup Set Sample is shown above the scroll bar There is no limit to the number of ex ante forecasts To increase the maximum select it then close and re open the dialog However in models containing exogenous variables other than the trend and GARCH_M terms 109 James Davidson 2008 the limit is set by the available post sample observations FORECAST TYPE 4 5 6 Ex ante multi step forecasts use the lagged forecast values to projected two or more steps forward Ex
148. led in Setup Estimation and Sample it also permits estimation by the three stage least squares 3SLS and the seemingly unrelated regressions SUR system estimators Select the type of estimator required under Select Estimator Note that the options depend on whether the System of Equations checkbox is checked For IV estimation select the instruments in the Model Select Instruments dialog dd Use the radio buttons to choose whether to specify the dependent variable s or regressors of Types 1 or 2 Then click on the variable s desired in the list Any number of regressors of either type can be selected but only one dependent variable unless the Systems of Equations box is checked in Setup Estimation and Sample k Set the Lags scrollbar to automatically include lags up to the set order of all variables of the Type whose radio button is currently selected Use the check boxes to include an intercept and or a trend dummy Use the check box to enable a Wald test of parameter constraints The type of test is specified in Model Parameter Constraints press the square button to open this dialog Parameters for zero and linear restrictions must be specified in the Values Equation dialog 57 James Davidson 2008 Notes Enable the Cointegrating Regression options by checking the checkbox Then o check either or both of the Cointegration Test checkboxes to compute the residual Phillips Perron and or augmente
149. leted it will be necessary to either restore the Results location or move the licence file manually to the new one TSM reads the licence file at start up and looks for it in the current Results folder first If it is not found there the program looks in the TSM Home directory If a licence file exists in the current Results folder it will take precedence and any licence file stored in the TSM Home directory will be ignored To see the latter registration change the Results folder 129 James Davidson 2008 10 Interpreting the Output PARAMETER LABELLING 1 The symbols ARI AR2 MA1 MA2 are used to label the ARMA coefficients in the output The prefixes GARCH EGARCH or APARCH as appropriate are appended for the conditional variance coefficients in the default case of the ARMA in squares parameterization For the standard Bollerslev parameterization AR and MA are replaced by Alpha and Beta respectively These notations are also used for the BEKK multivariate GARCH model Be careful to interpret the latter parameters correctly For models specified in the Model Dynamic Equation dialog the Type of a regressor appears as a prefix in square brackets for example 1 Varl1 denotes that Varl is a regressor of Type 1 This prefix is omitted if only Type 1 regressors are specified and also in equations specified in the Model Linear Regression dialog Note in the latter case the Type only
150. levels Note id Any Type 1 regressors included are differenced along with the dependent variable s If a trend is included it becomes in effect an intercept for the differenced model A Type 1 intercept is unidentified and is not permitted A Type 2 intercept can enter as an alternative to the trend but will be suppressed if a trend is specified FR Type 2 and Type 3 regressors enter as usual and are not differenced Lagged dependent variables included as either simple regressors of Type 2 or as components of equilibrium relations are not differenced X In fractional cointegration models the program modifies the reported value s of d3 in the appropriate way such that 1 is added to the order of difference d1 as reported Use the Values button to open the relevant Values dialogs and update them with new settings if already open Use the Clear button to remove all selections in this dialog The Go button launches an estimation run duplicates the Run button and Actions Run Estimation VARIABLE SELECTION T The three regressor Types correspond to the vectors denoted x_1t x_2t and x_3t in equation 3 1 of the main document Therefore the estimated coefficient of a particular regressor can be different depending its Type when AR and or MA components are specified Type 1 and 2 intercepts must be interpreted similarly When one or more variables are selected in any category the corresponding radio button is hig
151. lling parameter estimates are displayed with 2 standard error bands the usual regression standard errors with covariance matrix formula selected in Options Tests and Diagnostics 9 The Fill symbol option is used for probability and variance plots That is the region between the plotted line and the time axis is shaded light gray If for any reason a different plot style is required for these series use the Retrieve Series command to add them to the data set then plot using the options in Graphics Show Data Graphic 10 Select the type of plot desired for confidence and standard error bands in forecasts and recursive rolling estimation none bands or bars in Options Graphics Options 7 3 Graphics Monte Carlo Graphics The frequency distributions generated by Monte Carlo experiments can be 98 O James Davidson 2008 displayed as kernel densities and histograms Cumulative frequencies can also be displayed as an option ll Select plots for display by clicking on the list or pressing Select All Unselect an item by clicking again Remove all selections with Clear Plot selected items by pressing Plot Double clicking a list item displays the plot but does not leave the item highlighted k The graphic display dialog opens automatically at the completion of a Monte Carlo run Alternatively open it from the menu with Graphics Monte Carlo Distributions Zi The bandwidth used to compute the kernel density
152. lso the transition weights If Markov switching regimes are specified also The filter probabilities a The smoothed probabilities For explained switching models the transition probabilities for Regimes to M 1 In regime switching models the residuals are computed as weighted averages of the regimes using the filter probabilities as weights Note In the case of the Probit model generalized residuals replace variance adjusted residuals EXPORTING AND PRINTING LISTINGS 3 The Export Listings option controls the export of the items listed under 2 Select a radio button for the type of spreadsheet file or ASCII file to save The files are identified by a descriptive name and the current run ID Check the checkbox Save Listings Automatically to have all the series associated with an estimation run saved to a file of the selected type If this box is not checked specific outputs from the latest run can be saved individually as required by selecting the menu items under File Listings To distinguish sample and ex post forecast periods in the output file an extra column is printed with an indicator variable 0 sample forecast Check the boxes in Print to Results Window to have the items appear on the screen Large screen listings are best avoided since the results window buffer may fill up rapidly RETRIEVING GENERATED SERIES T7 Retrieving series means adding them to the current data set for further ana
153. lt These will not match the naive conventional standard error formulae reported by most packages and note that the latter are often based on incorrect assumptions although they can always be computed as an option Heteroscedasticity and autocorrelation consistent HAC 13 James Davidson 2008 standard errors are also optionally available Test p values and confidence intervals can also be computed by the parametric bootstrap based on resampling model residuals and using the fitted model to simulate data under the null hypothesis Asymptotic chi squared statistics are reported by default for the standard tests of restrictions and mis specification although reporting in F statistic form 1s a selectable option Note that in most time series applications F statistics are not truly F distributed in finite samples Bootstrap p values can be computed if desired for improved test performance in small samples Another approach related to the bootstrap is to tabulate test statistics by simulation and use the EDF tabulations to generate p values 0 2 How To For the first time user who doesn t want to spend too much time with the user s manual here are some simple step by step instructions to get you started 1 HOW TO LOAD A DATA SET Click the Open File button on the tool bar In the file dialog navigate to the Windows folder containing your file in the usual way and click on it Several different file formats are suppo
154. lysis in the program The radio buttons allow you to choose whether to retrieve the next run only and then cancel the option or keep it selected The series are allocated standard names with numbers appended to distinguish successive retrievals They can be renamed more descriptively in the Data Transformations dialog if desired 8 2 Options Tests and Diagnostics 1 Unless otherwise indicated the test statistics controlled through this dialog are by default asymptotically Chi squared with degrees of freedom shown in parentheses The nominal p values of the tests are shown enclosed in braces following the statistic values F versions of the tests can be optionally substituted Q TESTS FOR SERIAL DEPENDENCE Ze Q tests for autocorrelation in levels and squares are printed after every estimation run The upper limits to the Q test order and correlogram order are set at number of observations 3 In models where variance adjusted residuals are defined GARCH regime switching the Q 104 O James Davidson 2008 3 statistics are computed for these series Check the Ljung Box radio button to use the Ljung Box 1978 formula for the Q statistic otherwise the Box Pierce 1970 formula the default DIAGNOSTIC TESTS 4 Preset diagnostic tests are available in score test and conditional moment test versions The option of printing the F forms of the diagnostic tests can be selected with the check box This provide
155. m where denotes the ID number of the last run Enabling this option allows an earlier estimation run to be re created instantly by loading the requisite file see 2 1 File Settings Open The currently stored results estimation output graphs series Monte Carlo results etc can be saved in the settings file at closedown along with the settings and model specifications This means that the last estimation results can be redisplayed without having to be recomputed Click the Evaluation button then Yes The program is in almost exactly the same state as at the last closedown but the complete contents of the results window are not stored Save these in the usual manner Enabling the option Delete Temporary Files on Exit will cause TSD model results and data files to be deleted automatically at the end of a session Uncheck this if you wish to keep your model results or check 1t to avoid excessive clutter in your working directory Data descriptions are saved as series name extensions that may not be compatible with other programs Set the option Omit Data Descriptions when exporting data for use in other packages Automatically Close Options Dialogs is selected by default and has the effect of closing any options dialog currently open when another is opened This saves a proliferation of open dialogs on the screen but can be disabled if it is desired to work on two or more options dialogs at once DISPLAY SETT
156. me estimators GARCH and Markov switching options are unavailable with least squares and GMM E Systems of equations are unavailable with skewed Student errors and all discrete data options i The Whittle method is only implemented for univariate ARFIMA models 2 If no conditional heteroscedasticity or regime switching features are specified the difference between Least Squares LGV and Gaussian ML is that in the latter case the error variance or covariance matrix for systems is estimated jointly with the other parameters 61 James Davidson 2008 Multi stage GMM with efficient weights matrix based on first stage residuals 1s effected by running the estimation repeatedly See Actions Run Estimation For this option to be active the type of covariance matrix desired Robust or HAC must be selected in Options Test and Diagnostics Options If Standard is selected only one step GMM is available Binary data means that the dependent variable may take only two values zero and one Count data means that the dependent variable may take only zero or positive integer values MODEL SPECIFICATION 5 Check the Impose Unit Root option to estimate an ARIMA p 1 q model and also an ARFIMA p 1 d q where 0 5 lt d lt 0 5 This option is distinct from performing the estimation on the pre differenced series because the regression statistics plots and forecasts are all generated for the original series of
157. metimes called an Error Correction Model ECM Most often an Eq R has the interpretation of a cointegrating relation in a system of I 1 variables although it could also in principle appear in a model of stationary processes Eq R s can also appear in single equations in which case they implement a re parameterization of the dynamic model in ECM form a Choose one of the three options for specifying the equilibrium relation s A Select Linear Equilibrium Relations to specify the relation s by choosing variables from the list B Select Nonlinear AR Closed VECM to include the set of dependent variables as lagged regressors automatically C Select Coded Equilibrium Relations to specify nonlinear equilibrium relations using the Coded Function dialog Use the first scroll bar to select the number of Eq R s to be included in the model dj Use the second scroll bar to chose the lag to apply to the Eq R s must be gt 0 Restrictions on each relation are set up in the Values Equilibrium Relations dialog 77 James Davidson 2008 Notes Options A and B 1 Every Eq R must contain at least one fixed coefficient otherwise the relation will be unidentified Set the fix in the Values Equilibrium Relations dialog If no restriction is set manually the first coefficient in the list will automatically have its coefficient set to 1 when the estimation is run Note The Values button is highlighted if two or more
158. mmon frame Line styles only apply to time plots 96 James Davidson 2008 10 11 12 This option over rides the Multiple Series Display setting in Options Graphics Line styles can be edited in Options Graphics The Scale on Right Axis checkbox is enabled when two or more series are selected If checked the series with the largest line number is plotted against the right hand axis If more than two series are selected all the others are plotted against the left hand axis as usual The Centre and Standardize checkboxes allow the variables to be relocated and rescaled for comparability Centre subtracts the mean and Standardize also divides by the standard deviation If the line type for Line 8 is chosen as Band Fill the selected variable is used to divide the sample into regimes If the selected variable is positive the regime is On and if the selected variable is zero or negative the regime is Off The observations of the On regime are indicated by light gray shading in the plot Typically the indicator variable would be a zero one dummy NOTE Only Line 8 can be given the Band Fill style 7 2 Graphics Equation Graphics The following items can be plotted following an estimation run x o RES Notes Actual and fitted series submenu time and scatter plots Residuals sub menu Variance adjusted residuals sub menu Conditional variances GARCH and regime switching
159. models only Regime probabilities sub menu regime switching models only All the time plots for the model in one frame Equilibrium relations sub menu error correction models only Ex ante forecasts sub menu Solved moving average coefficients impulse response and step response submenu A 2D or 3D plot of the criterion function if computed see Actions Plot Criterion Grid Plots of the recursive or rolling estimations if computed dialog Kernel density plots of the bootstrap distributions of parameter estimates and test statistics In the Residuals Adjusted Residuals and Equilibrium Relations submenus the available options are time plot correlogram spectrum correlogram and spectrum of absolute values histogram and kernel density and normal QQ plot There is an option to display all the representations in the same frame The Actual vs Fitted scatter plot includes the Fitted vs Fitted line which has slope 1 by construction and passes through the point of sample means The residuals correspond to the vertical deviations around this line but 97 James Davidson 2008 ordered by magnitude of the fitted values instead of the sample time ordering 3 Regime probabilities are summed over lags in Hamilton s switching model Smoothed regime probabilities are computed by Kim s algorithm see Kim and Nelson 1999 pp68 70 When switching probabilities are explained by exogenous variables both filter probabilities and t
160. n 2008 7 To modify the specification of an equation first open the corresponding Values dialog Use the choice widget appearing on the tool bar to switch between equations To exclude a regressor or lag from an equation select the Fixed checkbox for the parameter s in question and then make sure that 0 is entered in the Values field If desired any other fixed value can be set 8 Variables selected as endogenous can also appear on the right hand sides of the equations as Type 1 regressors to allow a simultaneous system Three Stage Least Squares can be selected as an option in the Model Linear Regression dialog In the Dynamic Equation dialog the presence of such variables automatically causes the FIML estimator to be computed provided suitable identifying restrictions have been imposed on the equations See the relevant help pages for further details 9 Equilibrium relations can be embedded in systems of equations to create an error correction model or cointegrating VAR The Model Equilibrium Relations dialog allows the selection only of a set of variables to be included in all the relations The Values dialog is used to impose restrictions which must include a normalizing restriction fixed at 1 typically on one variable 4 1 Model Linear Regression This dialog is for specifying a linear equation for estimation by Ordinary Least Squares OLS or Instrumental Variables IV 2SLS When a system of equations is enab
161. n ASCII files for reading only Data Descriptions opens a list of names of the currently loaded variables followed by any description that has been created for the variable The description is preceded by the symbol Register this Copy opens a dialog to enter the user s name and the unlocking key provided to registered users of the software About opens a box showing copyright information and the registered username USER S MANUAL 1 Navigate the User s Manual by the menu sections and sub menus subsections and also by clicking the Previous and Next buttons to move backwards and forwards through the pages These pages duplicate the contents of the PDF file tsmod4ghp pdf which is accessible through the Start Menu Windows VIEW TEXT FILES Ze 3 File Dialog opens the file dialog to select any ASCII file for reading Most Recently Opened repeats the last selection By default if no file has yet been opened it opens notes txt if this file exists Imported Ox Code refers to a source code file with ox extension which has been loaded from a distributed settings tsm file A distributor of coded functions has this opportunity to document their code by including text comments in the file before the code statements The code itself can also be inspected DESCRIPTIONS 5 Data descriptions can be created in two ways In Setup Data Editing and Transformations the choice widget item D
162. n also be inserted in Microsoft Word documents TSM saves data and graphics in a variety of other optional formats See 2 2 File Data 8 1 Options Output and Retrieval and 8 5 Options Graphics for details 12 Hints and Tips Here are some non obvious pointers for getting the best results from the program 135 James Davidson 2008 Suggestions from users for further tips are always welcome NUMERICAL OPTIMIZATION 1 TSM s optimization algorithm uses numerical derivatives which under certain circumstances can give rise to problems with successful convergence Its success can greatly depend on the good choice of starting values Analytic derivatives while more reliable would be difficult to implement for the wide range of nonlinear models offered by the program Some packages implement elaborate schemes to choose starting values automatically for specific models such as ARIMAs but again this type of strategy is difficult to combine with a wide range of models TSM implements a number of basic strategies but these cannot entirely replace the user s initiative in exploring the parameter space to achieve successful optimization The program makes a maximum of two attempts to perform an optimization where the second attempt uses the default starting values If both attempts fail there are several program settings that may assist A Enable the parameter rescaling option in Options Optimization and Run Set the v
163. n doubt 11 12 13 The GARCH M likelihood is computed by Gauss Seidel iteration of equations 1 and 41 or 1 and 42 for EGARCH A fixed number of iterations is used the default is 5 Increasing the number will increase computation time but may not improve the estimates significantly To stabilize the GARCH M calculations h_t or h_t 1 2 is trimmed before inclusion in equation 1 The upper bound is set to a multiple of the sample variance or standard deviation of the data called the trimming factor Try reducing this setting in case of failure of the algorithm The EGARCH likelihood can be computed in one of two ways direct nonlinear recursion of equation 42 default and Gauss Seidel iteration 1 e repeatedly solving the linear difference equation obtained by conditioning on h_t 1 2 in equation 42 There may be small differences between the two estimates due to treatment of initial conditions The main consideration in this choice is one of speed The nonlinear equation cannot be solved using Ox s vector manipulation capability and has to be programmed as a loop This could result in long solution times in large samples and the iterative method will often be quicker A convergence criterion is used to control the G S iterations The default maximum number 50 should not need changing 8 7 Options Optimization and Run OPTIMAND CONVENTION 1 Two of the estimators available least squares and GM
164. n several dialogs The action of the toolbar button can vary depending on the dialog currently open 3 COMPUTING ESTIMATES TESTS AND FORECASTS The basic method of operation is as follows 1 Specify the calculations and settings desired using the Setup Model Values and Options menus 2 Launch the estimation module using one of the commands on the Actions menu a dialog button or a tool bar button Both the Running Man and the Calculator buttons on the tool bar launch closed form non iterative estimations such as OLS and IV and associated tests and forecasts For nonlinear estimation if enabled the Running Man button launches the optimization algorithm while the Calculator button just performs post estimation computations forecasts or tests using the currently stored parameter values either obtained on the latest run or entered by the user 9 James Davidson 2008 NOTE forecasts and tests are not computed by merely specifying them in the Options dialog Use the menu items in the Actions menu for this purpose The Calculate button performs all the currently specified calculations and generates the complete estimation output for the current parameter values Each run has a unique ID number to identify the outputs associated with it such as graphics files spreadsheet files and settings files 4 SAVING PROGRAM SETTINGS TSM has a large number of optional settings that most users will want to change only occasionally
165. n the name fields below Notes 1 See Section 1 5 General Entering Formulae for detailed instructions on entering codes into the text field 2 Parameters removed from the equation are not deleted automatically but are suspended Clear the name field manually to delete a parameter permanently from the model 3 Increase the Maximum Parameters value and refresh the dialog to display additional fields TYPES OF FORMULAE Equation The equation is entered explicitly in the format Formula where the formula corresponds to the explained part of the model and implicitly the dependent variable named in the heading appears on the left of the The residuals corresponding to the function f1 in equation 3 29 of the main document are computed as the difference between the left and right hand sides of the equation Use this style whenever the model can be represented in the form required which is most cases Residual Enter an expression which itself equates implicitly to the residuals of the model f1 in equation 3 29 In this case no sign 68 James Davidson 2008 should appear in the formula The purpose of this option is to allow models in which the dependent variable s enter s nonlinearly Since the model cannot be solved automatically no Actual Fitted plots forecasts or simulations are available in this case This option is also used for the formulation of equilibrium relations for ECM models
166. n vector ARMA and GARCH models specified in the Dynamic Equation dialog the lags of all the variables are included by default in each equation For example a VAR 2 system of three equations has 6 regressors in each equation Of course some of these regressors can be suppressed if desired by fixing their coefficients at 0 in the Values dialogs Note that a VAR can be set up in either the Linear Regression dialog or the Dynamic Equation dialog In the first case it will be estimated in two steps by SUR equivalently OLS if unrestricted In the second case it will be estimated numerically by Least Generalized Variance or ML 15 OUTPUT CONVENTIONS The outputs from TSM are not always the same as those of other packages t ratios and p values are not reported in those cases where zero is not the natural null hypothesis for the parameter variances for example The Durbin Watson statistic is not reported by default since it is often not valid in dynamic regressions See the Tests and Diagnostics Options dialog to select it A valid LM statistic or M statistic for residual autocorrelation or neglected ARCH can always be computed if desired and provides an equivalent test to the DW in those cases where it is valid Autocorrelation Q statistics for residuals and squared residuals are reported by default as are standard model selection criteria although these outputs can be optionally suppressed Robust standard errors are reported by defau
167. nd append these lines to a designated file 2 Have all the output saved automatically to a file in the background Both methods can be used at the same time if desired The available commands are Enable Background Saving Switches on Background Save mode Disable Background Saving Switches off Background Save mode New Results File Opens the file selection dialog Choice can be an existing text file or a new one Locate Results Folder File Show change the current path to the folder for results and graphics Optionally show change the results file name Notes 1 Results are always appended to a file To start a new file choose a new name or delete the existing file first 2 The default results file is tsmresults txt in the working directory This will be created automatically if it does not exist There is no default name for selections You are prompted for a file name if one is not currently specified If background saving is enabled the New Results File command designates a new file for background saving If background saving is disabled the chosen file will be used for selected text 3 If the directory for a new results file is different from the current working directory the working directory is changed accordingly Listings files and graphics will be saved thereafter to the same location However the settings file must always reside in the Start in directory so it can be found at launch 4 To guard
168. ndividual option is selected only the series for the equation selected in the Equation choice widget on the tool bar is plotted LINES AND SYMBOLS 14 Series can be plotted by lines connecting the data points default by symbols at the points or by both This is a general setting The choice of colours and styles for each line can be selected in the Line Styles area Note that the selection of symbols can be overridden for individual lines by choosing None in the symbol choice widget LEGENDS 15 16 Legends are used to label series when two or more appear in the same frame otherwise the series name appears as the plot title There are five options for placing the legend in the frame X No legend TL Top left corner default TR Top right corner BL Bottom left corner BR Bottom right corner Note that these are general settings It is not possible to place the legend differently in different plots in the same frame Check the Box checkbox to enclose the legend in a box By default no box is shown CRITERION PLOTS 17 There are three options for the plot created by Actions Plot Criterion Grid If both is selected the resulting plot is the same as the surface plot with contours drawn on the floor p_1 p_2 plane of the three dimensional graph DENSITY PLOTS 18 These plots are available under Resampling Distributions to display bootstrap and subsampling distributions Monte Carlo Dist
169. ng the simulation of the fitted model with the original data can be a useful informal diagnostic tool However the main application for the simulation module is to running bootstrap tests and Monte Carlo experiments A flexible interactive Monte Carlo module is provided 7 MODELS A model is a complete set of specifications and values to estimate simulate or forecast an equation or system of equations Any number of these specifications can be stored and recalled during a session as well as saved permanently in the settings tsm file For example this option allows the user to run an exploratory regression on the fly while working on a complex multiple equation model without losing any settings and values Just use the Model Manager to store the current settings and values to a named model optionally including the data set Load the model to restore them again The generated series graphics and optionally data set associated with a model are stored in a file with tsd extension and blue TSM Windows icon Models are also used for running Monte Carlo experiments Select one model 10 James Davidson 2008 to generate the data using the simulation module and another or the same model for estimating allowing a very flexible approach to misspecification analysis 8 PROGRAMMING WITH TSM TSM can be called as a module in your own Ox program It is easy to write out the commands and options set by TSM dialogs as lines of Ox co
170. not a general to specific search nor specific to general but in fact both The limitation is that it cannot feasibly examine such large model spaces some other automatic specification search packages that are currently available which are 87 James Davidson 2008 selective in the cases they examine 4 The procedure can be used with any model except regime switching including equation systems although it only searches over regressor choices Any other model features will correspond to the baseline specification and the search is conditional on these Note that the number of models needing to be estimated may be very large For example with 4 variables and 4 lags current values N 20 and the choice is over 2420 1048576 cases This is feasible for OLS but probably not for iterative estimation 5 There is no option to print all the estimation results The output includes the baseline model and the optimal case 6 5 Actions Recursive Rolling Estimation This option estimates the same model for a succession of samples either of increasing size with fixed starting point incremental estimation or fixed size with moving starting point rolling estimation We call these procedures recursive estimation and while they are not recursive in the strict sense of using an updating formula to modify the estimator with the extra observation at each step it is computed afresh the current estimates provide starting values for eac
171. ns for model parameters can be set Among the uses of these dialogs are Setting starting values for numerical optimization Fixing parameters at chosen values during estimation iS Setting inequality constraints on parameters during estimation Setting zero or linear restrictions on parameters either for constrained estimation or calculation of Wald tests The Values dialogs can be accessed from the menu bar or by the Values button in the relevant model specification dialog Parameter values obtained in the latest estimation run can be viewed in the Values dialogs and will form the starting values for the next run unless edited or cleared Alternatively the menu item Evaluate at Current Values or the Calculator button generates the program outputs at these values without re optimizing 13 CODED FUNCTIONS General nonlinear models can be estimated by creating coded formulae The program features a formula parser which can evaluate functions of data and or parameters typed using standard notations This feature is used to create functions for estimation and parameter restrictions for testing as well as data transformations Alternatively TSM can estimate a model programmed by the user in the Ox language while making use of all the estimation testing and forecasting features of the package This feature is distinct from though compatible with calling TSM from within an Ox program 12 O James Davidson 2008 14 SYST
172. ntly stored in the Values fields Note that these are the estimates following an estimation run This option can be used for example to obtain test statistics forecasts listings etc for a model that has just been estimated without repeating the optimization Notes 1 This command is also launched by the Evaluate button on the toolbar 2 If Linear Regression or Cointegration Analysis dialogs are open the command has the same effect as the Go buttons and Actions Run Estimation 6 3 Actions Estimate Multiple ARMA Models Estimates a sequence of models with increasing ARMA orders starting with ARMA O 0 All other features of the model are as currently specified 86 James Davidson 2008 although regime switching options are disabled The limits of the sequence are set in the Setup Multiple ARMA Models dialog Notes 1 Starting values are set to either the estimates from the preceding specification or zero as appropriate The ARFIMA 0 d 0 is initialized with Robinson s 1994 nonparametric estimator of d Ze Other selected model features regressors conditional heteroscedasticity supplied function are estimated as usual with the supplied starting values for each case 3 Post estimation options forecasts correlograms graphics impulse responses tests series output and retrieval are suspended Re estimate the selected model to get these outputs 4 This option cannot be used in conjunction with regime
173. o 0 and then create the one period lag in Setup Data Transformation and Editing Include this variable as a Type 2 with Lags set to the desired maximum 3 A confirmation box opens to guard against accidental launches This reminds you what selection criterion is currently chosen MULTIPLE ARMA MODELS When this option is selected in the Actions menu or by pressing the Run Multiple ARMA button the program automatically estimates all the ARMA p q or ARFIMA p d q specifications for all values of p and q in the indicated ranges 45 James Davidson 2008 Enter max p max q and max p q in the text fields provided With the default settings all entries 2 the program estimates the following cases of p q in the order shown 0 0 1 0 2 0 0 1 1 1 0 2 A confirmation box appears to guard against accidental launches See Actions Estimate Multiple ARMA Models for additional details 3 5 Setup Recursive Rolling Estimation This dialog sets up the options for recursive estimation For details on the output produced by this option see Contents Actions Menu Recursive Rolling Estimation Choose rolling estimation fixed sample size or incremental estimation extending sample size with the radio buttons Set the initial sample in the usual way as the usual estimation sample Access the Set Sample dialog either using the button provided or in Setup Set Sample or a model dialog Step size is t
174. o may not be used in parameter constraints This results in a parsing error Also note pos x y y max x y neg x y y min x y x y flr x y x mod y x y integers 1 ips y x 1 if y lt x 0 otherwise etc etc Other uses include creating period dummies If t is an integer dummy neg pos Trend t 1 1 0 up to date t 1 from date t onwards 11 Reminder the following uses are mandatory Parentheses for function arguments and sub formulae el Square brackets for parameter variable numbers e Braces for lags and leads 12 Ifthe formula cannot be parsed e g non matching parentheses missing operators an error message is printed and the calculations are terminated If an operation is illegal e g square root of negative number the output of the formula will be NaN RESERVED NAMES 13 The parameter names U u and N n are reserved and are treated differently depending on the function call In estimation runs they are assigned the value 0 In simulation runs and 24 James Davidson 2008 14 15 data transformations U and u are replaced by a uniform 0 1 random drawing and N and n are replaced by a standard normal random drawing This feature is primarily to allow the generation of randomized models for e g test power evaluation The variable names E j e j where j represents a positive integer are reserved for use in recursive functions They are replaced b
175. o print a table of summary statistics Alternatively just double click the variable Optionally the following tests for integration order 1 0 or I 1 are computed X Lo s 1991 R S test for I 0 against I d for d gt 0ord lt 0 A bounding p value probability of the statistic exceeding the computed value under HO is given in braces T The Kwiatkowski et al 1992 KPSS test of I 0 against I 1 A bounding p value probability of the statistic exceeding the computed value under HO is given in braces The Harris McCabe Leybourne 2006 N 0 1 test of short memory see 8 2 Options Tests and Diagnostics for additional details Phillips Perron 1988 test of I 1 against 10 A bounding p value probability of the statistic lying below the computed value under HO is given in braces l The augmented Dickey Fuller test of I 1 against 1 0 The number of lags is chosen to optimize the Schwarz information criterion over the range 0 to 1 3 Robinson s semiparametric estimator of d See Robinson Anns Stat 22 1994 515 539 The statistic corresponds to eq 4 2 of the paper with lamda_m 2 pin 0 35 and q 0 5 Notes l Check the Detrend box to compute the statistics for the series after detrending by OLS 2 Check the Differenced box to compute the statistics for the differenced series in addition to the undifferenced series 3 Choose the order of correlograms of the series and squared series with
176. omly resampled residuals or computer generated shocks The simulation module is the basis for nonlinear forecasting bootstrap testing and Monte Carlo experiments To gain insight into the properties of an estimator it is always a helpful exercise to apply it to artificial data from a known model To create an artificial sample do the following 1 Clear the data File Data Clear 2 Set a sample size In Setup Data Transformation and Editing choose Edit scroll down to Re Size Sample enter a value and press Go A variable called Zeros with the specified number of observations is automatically created 3 Open Options Simulation and Resampling and choose a shock distribution either Gaussian or Model In the first case also set the shock variance In the second case a likelihood function must be specified in Model Dynamic Equation 4 Set the model specifications in the usual way selecting Zeros as the dependent variable Pre sample values are used to start a dynamic simulation and if desired these can be inserted in Zeros in Setup Data Transformation and Editing 5 Enter parameter values in the relevant Values dialogs Don t forget variance parameters in the case of Model shocks 6 Open the Model Manager and save your specifications under a suitable name 7 Select Actions Simulate Current Model and add the artificial data to the data set if desired 8 Alternatively use your model to set up a Monte C
177. on dialog are done numerically The optimization routine is the Ox implementation of the Broyden Fletcher Goldfarb Shanno BFGS quasi Newton procedure with numerical derivatives This method reports strong convergence in a high proportion of cases However don t assume that the message Strong convergence means that the estimation criterion has been globally optimized It simply means that a local optimum has been found Restarting the search algorithm from different points is the only way to confirm a global optimum The messages Weak convergence or No convergence may also be returned by the search algorithm A run may also terminate with the message Estimation failed Algorithm returns NaN or infinity This typically indicates overflows in the floating point calculations e g dividing by zero or attempting to take the logarithm of a negative number probably due to inappropriate starting values If this occurs optimization is restarted automatically at the default parameter values This will often clear a problem with bad starting values GRAPHICS FOR REGIME SWITCHING MODELS 19 20 For simple Markov and Hamilton switching models the M 1 series of independent filter probabilities can be listed and or plotted These are the probabilities of the regime being occupied conditional on information to date t as used to weight the likelihood terms in estimation In the case of Hamilton s model these are summed over lags p to
178. ood or other criterion function numerically using the BFGS and or simulated annealing algorithms Model choices include Gaussian Student t and GED continuous distributions binary logit and probit models and count data models All these models can feature conditional variances and Markov switching or smooth transition nonlinearity 10 SELECTING VARIABLES Model specification dialogs include a list of variable names corresponding to the currently loaded data file Selecting a variable is a two step procedure First select a radio button specifying the variable Type dependent variable s one of several types of explanatory variables instruments and so forth Next click on the desired name in the list to highlight it The list can be scrolled if it is too long to display complete in the dialog Note that when one or more variables are selected in a category the corresponding radio button is highlighted with a lighter grey panel To see which variables are currently selected in a particular category click on the radio button in question A little practice helps to get variable selection smooth and rapid and it is a good idea to click on each highlighted button in turn to check the specification is as desired before launching the estimation run To deselect a variable simply click on it again to remove the highlight There is also a Clear 11 O James Davidson 2008 button to remove all the current selections NOTE to display time plot
179. oose Paste To save text ina file first name the file with File Results New Results File Then select 137 James Davidson 2008 the desired text with the mouse and give the command File Results Save Selected Text Note that subsequent saves will be appended to the same file To avoid this behaviour give the New Results File command again to create or reinstate a results file ENTERING DATA BY HAND 12 13 14 Use one of the following methods to type data directly into the program The second method is recommended for entering several variables at once Don t forget to save the data set afterwards before doing anything else Use the Setup Data Transformation and Editing dialog to create a new variable If no data are currently loaded give the command Re Size Sample and enter the desired sample size in which case a new variable Zeros is created automatically Otherwise give the command Make Zeros Use Rename to change Zeros to the name of the new variable Then choose Edit List Compare select the first observation and press Edit Observation To enter successive observations type the values into the edit field and press OK repeatedly Alternatively type the data by observation either into a text editor or into the results window as described in 11 above The first line should contain two integers the number of observations lines to follow the first and the number of variables values on each line Separa
180. operational settings The models tsd files which can contain the associated data sets see Setup Model Manager should be located in the Start in or results directory of the installation so that they can be read 4 Models cannot be imported from settings files that have been created with the Export command nor from files that were created with the option Save Current Results with Settings checked in Options General In this case load a settings file and save it without these options before attempting to import from it Alternatively save and load the model specifications in text format see 8 below EXPORTING SETTINGS 5 The Export option allows model specifications to be distributed to other users This option has the following features X All relevant information is saved in the tsm file including the current data set s model listings usually saved in separate tsd files and supplied Ox code All local path information including MRU lists is omitted from the file l When the file is loaded the stored data and listings files are automatically saved in the local Start in directory In this way the local installation can exactly reproduce the set up existing on the machine where the export file was created 6 To be exported using Export supplied Ox code must be contained in one of the following locations 1 The standard file usercode ox located in the Start in directory 2 The file named
181. option is enabled by setting the Type I Fractional text box in Options General to a positive integer value corresponding to the number of generated regressors to be included In the output the estimated coefficients are denoted typelFrac Z1 typelFrac Z2 These are akin to principal components of the omitted stochastic terms 30 Recommended settings are for the number of components are or 2 The columns of higher order are very small so including too many may produce unstable results 4 3 Model Conditional Variance This dialog sets up the specifications for equations 5 1 5 2 or equations 6 1 6 2 of the main document In the latter case the specification set applies to the conditional variances of each equation Use the scroll bars to choose order of GARCH specification Use the radio buttons and checkboxes to select other model options 65 James Davidson 2008 Notes Use the radio buttons to switch between selection of the three possible types of GARCH regressor then click on the variable list to make the selections Distributed lags of the GARCH regressors can be specified using the Lags scrollbar just as in the conditional mean model Check the Abs checkbox to take absolute values of the regressors automatically This menu item is checked if a conditional variance model is specified Its settings are ignored unless a ML estimator is selected and Conditional Variance Model is checked in t
182. option provides a handy shortcut The program knows a regressor is a seasonal dummy if the string seasonal dummy or seasonal dummies is part of the data description This is set up automatically if the dummies are generated in Setup Data Transformations and Editing In equation systems all exogenous regressors of all types in all equations and in equilibrium relations are included in the test but intercepts trends and current and or lagged endogenous variables are excluded Endogenous means any variable explained by the system Additional parameters can be added to the test set in the usual way by checking the relevant Wald Test box in the Values dialogs Variables having parameters fixed are excluded from the test CODED_RESTRICTIONS 10 11 12 A coded restriction on the parameters is set up by typing the equation into a text field After selecting the restriction type with the radio button press the Code button to open the text box TEXT BOX CONTROLS Cancel Close box discarding changes Delete Delete the currently displayed formula Next Displays the next formula where present New Opens a new blank formula where there is no Next Previous Displays previous formula where present OK Closes the text box and stores current formulae Return Equivalent to pressing OK Closing the dialog with the Windows Close button x 1s equivalent to Cancel For information on entering formul
183. or models intended to be adapted to different data sets For example such a model may specify inputs for a user coded estimate or test Note If this option is selected the Store Data with Model and Store Results with Model options are disabled Stored models include the current settings for the Semiparametric Long Memory and Cointegration Analysis dialogs Different settings for these modules can therefore be stored and recalled in the same way as for the main equation specifications LOADING MODELS 11 12 13 Loading a model overwrites the current settings Store these first if they will be needed subsequently See 8 above press the Evaluate button to re display the estimation output if this has been saved with the model This saves time if re evaluating the results would be time consuming as when output of bootstrap inference is selected The data file specified in the model will be reloaded automatically provided it has not been deleted or moved It can have been edited or had series added to it but any variables that appear in the model must of course be present in the file otherwise an error occurs It is the user s responsibility to ensure this and the safest way is to check the Store Data with Model box so that a dedicated copy of the data is saved DEFAULTS 14 When program settings are cleared and restored to defaults a model called Defaults is created automatically It is recommended to s
184. or to include in the bilinear specification If set to zero this corresponds the usual AR F IMA p d q model id Use the other check boxes to select or deselect additional model features conditional variance model coded nonlinear function regime switching equilibrium relations and parameter constraints Press the button to the left of the checkbox to open the corresponding dialog if currently closed T For Instrumental Variables estimation IV GMM use the Choose Instruments button to open the selection dialog 5 The Sample button opens the Set Sample dialog Use this to select the observations to be used for estimation The setting is the same as if opened from Setup Set Sample Pressing the Simulate button allows the All Available Observations button to show the available sample of exogenous variables for a simulation of the dependent variable The Options button opens the most recently opened estimation options dialog from the Options menu By default this is the Tests and Diagnostics dialog Click the horizontal lt lt lt lt and gt gt gt gt bars in these dialogs to switch between options dialogs gt The Values button opens the equation Values dialog or refreshes it if it is already open To compute the estimates press the Go button This duplicates the Run button on the toolbar and the Actions Run Estimation menu item Notes ESTIMATION CRITERIA 1 Note limitations on the application of so
185. ory the specifications that the user has selected and either starting values entered or estimated values following an estimation run This dialog allows model specifications and results to be stored under identifying titles and subsequently recalled Material stored includes parameter estimates with information on restrictions or bounds estimation and testing options generated series forecasts recursive estimates and criterion plots The latter series can be used to produce additional plots and test statistics without re running the estimation Stored models are also used to set up Monte Carlo experiments Load Model Loads the model whose title is highlighted in the list Store Current Model Opens a text field for the entry of a model title To complete the entry and store the model either press Return or click the OK button otherwise click Cancel Model Description Opens a text box where details of the highlighted model can be entered by the user for later reference Click the button again to close the box Move Up Move Down Use these buttons to arrange the order of the models in the list Delete a Model Opens a confirmation box and removes the model whose title is currently highlighted in the list if the action is confirmed Clear All Models Opens a confirmation box and removes all models in the list if the action is confirmed 42 James Davidson 2008 STORING MODELS 1 By default the model title
186. out a rescaling transformation The transformation can be selected by the user in the Options ML and Dynamics dialog In certain cases raising the order of root from 2 to 4 may be found to aid 130 James Davidson 2008 convergence while in others 1 will work satisfactorily Similarly the parameter of the Student t distribution can optionally be estimated as a root of the degrees of freedom The square root is the default See the Options ML and Dynamics dialog to set alternative values This is again for reasons of numerical stability The parameter 1s both bounded below and infinite in the Gaussian case and extreme values are potentially difficult for numerical differentiation By setting the root to a negative value the inverse transformation can be applied such that the parameter is zero in the Gaussian case STANDARD ERRORS TEST STATISTICS AND P VALUES 9 10 11 12 Every estimated parameter is shown in the output with either its estimated standard error or the words Fixed or Solved when the parameters have been so designated in the Values dialogs Following the standard error most parameters show the t ratio and nominal p value of the significance test The degrees of freedom are calculated as sample size total model parameters number of equations Parameters for which there is no natural zero hypothesis to be tested such as the variance GARCH intercept Student s t degrees of freedom etc a
187. ow the result of each numerical 88 James Davidson 2008 optimization denotes strong convergence of the search algorithm denotes weak convergence of the search algorithm denotes failure to converge See the Ox documentation for the definitions of these cases This option has no effect in the case of non iterative estimation 6 6 Actions Plot Criterion Grid Use this option to create a contour plot of the concentrated criterion function Parameter bounds must be enabled in the Values Equation dialog The number of grid points selected in Options Optimization and Run The choice of parameters for plotting and the bounds of the grid are set in the appropriate Values dialog s The operation is carried out on the first one or two parameters satisfying the following conditions 1 the fixed flag is set 2 the upper bound exceeds the lower bound The criterion function is maximized with respect to all other parameters holding the selected one s at the grid values Normal output is suppressed A progress bar shows the progress of the calculations A choice of contour plot and surface plot is available for the 3D case set the option required in Options Graphics The maximum maximorum is indicated The criterion values can also be exported in a table Notes 1 Other parameters can be either fixed or free for this operation If a pair of grid bounds for a fixed parameter are both set to zero the parameter is tr
188. pen The variable selections Type 1 and 2 regressors are common to both An autoregression can be estimated either in this dialog numerically or as a linear regression by using the Lags feature see 5 above BILINEAR MODEL 15 Remember that if the bilinear order r is increased from 0 to 1 this adds p parameters to the model where p is the AR order However raising r further only adds one additional parameter at each step not p due to the imposed restrictions This is different behaviour from the commonly described unrestricted bilinear model NONLINEAR MOVING AVERAGE SPS 16 17 18 Selecting this feature replaces the error term Ut with the expression Ut Ut 1 alpha beta 1 exp gamma Ut 1 c1 Ut 1 c2 where alpha beta gamma cl and c2 are additional parameters Combine this option with an imposed unit root to get models which can switch stochastically between I 0 and I 1 Variants ii To implement a close approximation to the STOPBREAK model fix alpha 2 beta 2 cl c2 0 E To obtain the STIMA model fix gamma 100 or any sufficiently large value impose the constraint cl c2 Then alpha is the MA coefficient for small deviations Ut 11 lt c1 and alpha beta for large deviations Alternatively all the parameters can in principle be freely estimated Nonlinear MA models can also be implemented by coding the required 63 James Davidson 2008 formula see Models Code
189. pens the corresponding Values dialog or refreshes it with new settings if it is already open If any parameters are fixed in this dialog the button is highlighted as a reminder 2 The Clear button sets all specifications in the dialog to the defaults 3 The Go button where provided is an alternative way to launch an estimation equivalent to selecting the Run button on the toolbar or the Actions Run Estimation menu item 4 Where provided the Sample button opens the Setup Set Sample dialog 5 Where provided the Options button opens the last opened estimation options dialog from the Options menu By default this is the Tests and Diagnostics dialog Notes 1 Pressing the Options button repeatedly cycles through all the accessible options dialogs 2 Only relevant options are accessible from this button depending on whether it is located in the Linear Regression or Dynamic Equation dialog All options dialogs are accessible in the usual way through the menu or the gt gt gt and lt lt lt bars SPECIFYING SYSTEMS OF EQUATIONS 6 A system of equations is specified by checking this option in the main Model dialogs and then selecting a set of two or more dependent variables All the equations are given the same specifications AR MA components regressors etc The specification of individual equations is changed by selecting restrictions on individual parameters in the Values dialogs 56 James Davidso
190. pern a a AEE e E Ea E E 91 SPECIFIED DIAGNOSTIC TESTS msi 91 TEST FOR I 0 DEPENDENT VARIABLE o ccooooccccnoconononononononononononnnonnonnncnnnnnnncconnrnnnnnnncnnnnns 91 6 9 Actions Compute MOTE Casts ras dc 92 6 10 Actions REEVES 92 6 11 Actions Simulate Current Model oooononcccnnncccnoncccnoncccnoncnonnnnccnnncccnnncnonnncnnnns 93 6 12 Other Commands iii da 93 SET DEFAULT VALUES curas a tit 93 3 James Davidson 2008 CLEAR VALUES oia a 93 CLEAR RESULTS WINDOW cecenii ne aea aa a ie a i a 94 CEOSEAEL DIALOGS via a a Shula ca coast a a i 94 RESTORE DIALOGS cnini ne sides EE ds tale ld di EE da E aaee 94 A a a acs E a a E E tus 95 7 0 Graphics General Information oococnnocccnoncccnoncnononanononononononononccnnnnccnnnnccnnnnnss 95 7 1 Graphics Show Data Graphic A A RR 95 7 2 Graphics Equation Graphics a aden sedi shea dartphtse Wassices va ena anna dn oanees 97 7 3 Graphics Monte Carlo Graphics oooococnoncccnoncncnoncnonnnnnononcnnnnnncnnnnc cnn nccnnnnnos 98 Bf PU OMG a in E E E E E 101 8 0 Options General Information and DefaultS oooonnnnconnnnccnnnocccononccnnnnccnnnnoss 101 8 1 Options Output and Retrieval siii is 103 SAVING DATA FILES catorce 103 OUTPUTTING TABLES AND SERIES 00 ee ceccceeccesncecesecenceceseeeenceceeeeeneeceeeeeneeceseeteneeess 103 EXPORTING AND PRINTING LISTINGS 0000 ceeececssecesececeseceeeeeceaeeeeacecaeeeeneecsaeeeeneees 104 RETRIEVING GENERATED SERIES 1 00 ceeecessecesec
191. plication The distribution of any function of the data set coded by the user in Ox can be studied by simulation after using TSM s modelling facilities or user supplied code to generate the data 7 James Davidson 2008 TSM 4 16 In the Windows installation the program can now be started by simply clicking on a tsm settings file in Windows Explorer These files are identified by the TSM icon as for the Start Menu shortcuts A new File Import Models function allows model specifications to be copied from one settings file to another The File Export command is enhanced to save the data and listings files as part of the tsm file A single settings file can now record a complete working environment including data models graphs and parameter values and be opened by a single keystroke on a different installation When an exported file is opened the data and listing files are recreated automatically in the Start in directory Additional resampling options sieve AR bootstrap Scatter plots now show regression lines superimposed TSM 4 15 has a redesigned interface Here are the main changes from Versions 4 14 and earlier The Estimation and Sample dialog has been replaced with a simplified Set Sample dialog This no longer has a toolbar button but is accessible as a floating window in all the model specification dialogs Estimator selection buttons and System of Equations checkboxes are now located as
192. r graphically Graphics Ex Ante Forecasts Check the Display Forecasts Automatically checkbox to have the main graphs displayed immediately a forecast is run Use the Graphics menu to display plots individually and additional items such as Monte Carlo distribution plots IMPULSE RESPONSES 22 23 24 25 The impulse responses coefficients of the solved moving average process for levels and also conditional ARCH GARCH variances will be plotted according to the radio button setting in either impulse form or step cumulated form or with both plots on the same graph In a system of N equations the responses shown are those on a dependent variable of an impulse to its own shock process only N plots If the System checkbox is checked then the responses on each dependent variable of impulses to each shock process are calculated N 2 plots This checkbox has no effect in a single equation model There is no limit to the number of steps possible To increase the maximum select it and close open the dialog Only the own shock responses can be listed in the results window For a listing of the full set export the data to a listing file see File Listings Save MA Coefficients Note Only the impulse responses are exported Compute the step responses manually by cumulation if required 8 4 Options Simulation and Resampling SIMULATION OPTIONS 1 There are six ways to generate artificial shocks to dr
193. r is used to identify retrieved series and also listings 20 James Davidson 2008 graphics and settings files optionally generated in the run This makes it easy to verify which piece of output goes with which run at the end of a session The current ID is stored in the file settings tsm It is preserved when settings are restored to defaults File Settings New It is reset to O only when settings tsm is deleted The text size can be changed from the default of 12 point in the Options General dialog The window can be resized by dragging the corner with the mouse and also maximized to fill the screen Dialogs are displayed on top of the window In maximized display mode dialogs can conveniently be arranged on the right hand side of the screen with the results printed on the left hand side The command File Load Text File allows the window to be used as a text editor To save text highlight it and use the File Save Selected Text command The main intended purpose of this feature is to allow a user s code to be conveniently edited on the fly without needing to start up OxEdit The command File Restart closes and restarts the program in exactly its previous state including window contents allowing the amended code to be compiled 1 4 Dialogs Dialogs are where most interactions between user and program take place They contain objects of the following kinds Buttons To initiate actions including opening closing other
194. rated by running the command Evaluate at Current Values with appropriate options set 3 4 Setup Automatic Model Selection Two options for estimating a sequence of models automatically are controlled from this dialog Note that they cannot be run simultaneously AUTOMATIC REGRESSOR SELECTION When this option is selected in the Actions menu or by pressing the Run Regressor Selection button the program chooses the set of regressors to optimize the chosen model selection criterion out of the specified regressors in a baseline model The option is described in detail in 6 4 Actions Automatic Regressor Selection Use the checkboxes in this dialog to choose which regressor Types are to be included in the initial set to search over For example select focus variables to be included in every specification as Type 1 regressors and nuisance variables whose inclusion is optional as Type 2 regressors To conduct the search over the latter set only uncheck the box Include Type 1 Regressors and check the box Include Type 2 Regressors Notes 1 To set the selection criterion one of Akaike Schwarz and Hannan Quinn open Options Tests and Diagnostics and select the radio button under Model Selection Criterion This setting is also used for choosing lag lengths in ADF cointegration tests and Saikkonen Stock Watson efficient estimation Ze Tip to make the lags of a focus Type 1 variable optional set Type 1 lags t
195. re shown with standard error in parentheses but no p value Nominal p values are also given for quoted test statistics in many cases asymptotic chi squared statistics For tests with non standard distributions Dickey Fuller KPSS R S these are computed from the available tables Since the coverage is incomplete these results are shown as inequalities Thus lt 0 05 would denote that the p value is less than 0 05 leading to rejection at the 5 level according to the table The result lt 1 simply indicates that the statistic falls within the bounds of all the tabulated points The tables themselves are given as an appendix to the main document If standard errors and or test statistics print as NaN stands for not a number this means the Hessian matrix of the optimization criterion could not be inverted at the current point Typically this means the local optimum is not unique which will also cause convergence failure Lack of identification is a leading cause for example a Markov switching model with a zero probability regime When Print Covariance Matrix is selected in Options Output and Retrieval Options the Hessian matrix itself is printed in this case as a diagnostic aid Checking for zero rows and columns could indicate the source of the problem SELECTION CRITERIA AND SUMMARY STATISTICS 13 14 By default the model selection criteria Schwarz Hannan Quinn and Akaike are defined as maximand penalty There
196. relation matrix are generated by a common GARCH 1 1 type model The interpretation of the coefficients depends on the setting standard vs ARMA in squares form see Options ML and Dynamics In the first case the fitted parameters are alpha and beta in the second case they are delta alpha beta and beta Note 1 The DCC parameters are displayed in the Values Distribution dialog 66 O James Davidson 2008 10 11 12 2 The MA form setting in Options ML and Dynamics does not affect the DCC specification If a multiple equation model is specified the BEKK Multivariate Garch model can be selected This is the case K as defined by Engle and Kroner 1995 Be careful to interpret the parameters correctly in this case Selecting Equation i in the Values Conditional Variance dialog using the choice widget displays the ith columns of the Aj and Bj lag polynomial matrices and although note that these matrices really define the dynamic structure of the vectorized conditional covariance matrix Vec H_t See the main document for details of the model The estimates are reported in the results window in the same style Note Neither the MA form nor the GARCH form options Options ML and Dynamics affect the BEKK parameterization Evaluation of the DCC and BEKK likelihood functions both require T NxN matrix inversions where T is the sample size and N is the number of equations Function evaluation could therefore be very
197. ributions to show the empirical densities of the replicates and also under Ex Ante Forecasts to show Monte Carlo forecasts The basic plots show the kernel density estimate Optionally the plots can also show the histogram selected by default and the normal curve with matching mean and variance A further option is to plot the cumulative distribution function CDF in a companion frame LINE STYLES 19 Eight line styles for series plotting can be set by the user The selectable option are line colour or pattern for monochrome plots 119 James Davidson 2008 20 21 22 23 24 29 26 2i line width symbol type and symbol size First select the line to be styled with the radio buttons Then select options with the line and symbol choice widgets and line width and symbol size fields s Available line widths are 1 thinnest default to 6 thickest l Symbol size can have any positive value 1 is default Monochrome lines can take any width if solid X Patterned lines dots dashes etc are always of thickness 1 Press the Restore Defaults button to set all line settings to defaults The Colour Pattern widget shows different options depending on whether the Monochrome Plots option is selected Note that both settings colour and pattern are remembered Switching between colour and monochrome plots does not delete the options The eight line styles are can be selected for data series plot
198. rivation of this test assumes the criterion function 1s a log likelihood OTHER DIAGNOSTIC TESTS 14 15 The Information Matrix test is available only for estimation by Maximum Likelihood It compares the inverted information matrix with the robust covariance matrix estimator having k k 1 2 degrees of freedom when k parameters are estimated This can be used as a guide to correct model specification and can also indicate best choice of covariance matrix formula The Nyblom Hansen model stability test is available as a whole model test degrees of freedom equal to the number of fitted parameters including residual variance and optionally as one degree of freedom tests for 106 James Davidson 2008 16 1 7 18 individual the parameters Check the Indiv checkbox for the latter option These are not printed by default since the output is potentially bulky Note that the tests use the table given in Hansen 1990 and the p values are available in inequality form The Durbin Watson test is included only for heritage reasons It is asymptotically equivalent to the Box Pierce Q statistic for 1 lag The LM or CM tests for residual autocorrelation are recommended in a regression context Use the Coded Test checkbox to activate deactivate a test statistic that has been supplied by the user as Ox code see Appendix C This checkbox has the same function as the Test checkbox in the Model Coded Function dialog It is d
199. rnov statistic comparing the fit of the original data points to the bootstrap distribution is reported to aid the best choice of this value SIMULATION PRESAMPLE MODE 11 Ifa dynamic simulation run starts at observation 2 or later the initial observations can be generated in two ways either fixed or random If fixed the actual values of the selected dependent variable are used If random the sequence is randomly set in each replication using generated or resampled shocks and the specified model In other words the simulation actually initializes at date 1 whatever the nominal start date E If a partial sum process unit root is specified the cumulation begins at the start date not at date 0 The random presample option can be selected for Monte Carlo experiments Fixed actual values are always used for bootstrap tests and Monte Carlo forecasts The setting makes no difference if the simulation start date is 1 TYPE I FRACTIONAL PROCESSES 12 A fractional ARFIMA model has long memory and can depend significantly on remote pre sample influences If these processes are simulated by setting presample shocks to zero the type II model this changes the distribution of estimators and test statistics even in large samples The type I model can in principle be simulated by selecting the random presample option and setting a long presample period However the number of lags required for a good approximation may be exce
200. rrelations are estimated as additional parameters The variances may be modelled by ARCH and other processes by selecting the Conditional Variance Model feature These parameters variances and correlations can also be subject to regime switching 27 If current endogenous variables are included as Type regressors the FIML variant of the LGV and ML estimators is automatically selected That is the log determinant of the square matrix of coefficients is incorporated in the maximand Suitable identifying restrictions must be imposed on the coefficients for this option to proceed The coefficient of the normalized variable in each equation is automatically fixed at O in this case Note Endogenous variables specified as Type 2 regressors are ignored If lags are specified only the lagged values are included 28 Ina VARFIMA model it is possible to parameterize the fractional difference parameters for Equations 2 as the differences from the parameter of Equation 1 This makes it easy to constrain and test equality of the parameters across equations To select this option set the third checkbox in the Model Equilibrium Relations dialog This setting applies even if error correction terms are not specified ESTIMATING TYPE I V ARFIMA PROCESSES 29 Itis possible to correct for the omission of the presample data in a fractionally integrated model by including some generated regressors depending on the d and variance parameters This
201. rror calculations are terminated after 100 seconds has elapsed and only the point forecasts 74 James Davidson 2008 are reported for further steps A warning message is printed in this case The SE bands can also be omitted see Options Graphics 17 The ST model has two identical maxima of the likelihood since interchanging both the regimes and the sign of the smoothness parameter gamma yields the same likelihood by construction Be careful to interpret the estimates correctly 4 6 Model Parameter Constraints This dialog sets options for imposing restrictions on the coefficients Three types of restrictions can be set up a zero restrictions b multiple linear restrictions and c general restrictions specified as coded formulae In case b only the constants intercepts of the constraint functions are set in this dialog The linear functions themselves like the parameters for zeroing are set in the Values dialogs Restrictions can be implemented in either of two ways Tested on the unconstrained estimates using the Wald principle le Imposed in estimation In the latter case the LM test for the restrictions is computed if this option is selected in the Options Tests and Diagnostics dialog In this case any fixing restrictions on the parameters will be treated as part of the maintained model and not tested To test fixing restrictions make sure the Parameter Constraints option is deselected in Model
202. rted but an Excel worksheet is a popular choice The series should be stored in columns starting in column 2 with the first row of the spreadsheet containing the variable names 2 HOW TO PLOT DATA SERIES Click with the mouse on the variable list in any open dialog Click the Chart button on the toolbar to display plots of all the highlighted series on the list E Clicking the Chart button without first clicking a variable list opens the Graphics Show Data Graphic dialog 3 HOW TO RUN A SIMPLE REGRESSION Click on the regression scatter button to open the Linear Regression dialog In the Select Estimator box choose Ordinary Least Squares the default Choose the dependent variable from the list and highlight the name by clicking on it with the mouse At most one name can be selected at once Note that the radio button is highlighted to show you have made a selection In the Select Regressors panel click on the Type 1 radio button Then select the regressors from the list as for the dependent variable Any number of names can be selected The radio button is highlighted Click the check box for Intercept and if appropriate for Trend As To ensure your selection of variables is as you intend it s a good idea the click alternately on the highlighted radio buttons Note how your selections on the data list are highlighted in turn K Click the Go button in the dialog or the Running Man or Calculator buttons
203. s a dialog for selection of graphical representations time plot correlogram spectrum histogram and normal QQ plot of any variable in the data set SIMPLE PLOTTING Notes 1 Select the type s of plot required using the check boxes Select one or more names in the variable list Optionally select for the series to be either detrended by OLS or differenced before plotting Press Sample to open the Set Sample dialog and choose the sample required Press Go Alternatively just double click the name of any series convenient for a single plot Unselect a selected variable by clicking it second time Press Clear to 95 James Davidson 2008 unselect all selected variables Ze Double clicking a variable on the list just displays the plot Selecting with a single click and then pressing Go plots the variable s and leaves them selected 3 Up to 36 plots can be displayed on one page However with large numbers of plots the quality of the display is not too good 4 If only time plots are selected multiple plots can appear in one graph by selecting this option in Options Graphics see Multiple Series Display However if correlograms or other types of plot are selected plots appear in their own graphs in a common frame de If the Scatter Plot option is selected the first two highlighted variables in the list are plotted together the first on the list is assigned the vertical axis Y and th
204. s an alternative approximation to the asymptotic Chi Squared distribution Note that these tests are not exact except in special cases SCORE LM TESTS 5 The following pre set score tests are available In each case the score of the extended model at the null parameter values is tested The extensions are Autocorrelation lagged residuals in equation 1 Neglected ARCH lagged squared residuals in equation 2 or absolute normalized residuals in equation 3 if EGARCH is specified x Nonlinear Functional Form RESET Integer powers of the fitted values of the null model in equation 1 l Heteroscedasticity square of the fitted values in equations 2 3 AR common factors p lags of Type 1 regressors in a model with AR p errors specified The number of lags to be included and the order of polynomial in the fitted values can be selected with the scroll bars These statistics are indicated in the output by LM after the description If no conditional variance is specified in the null model the LM tests for neglected ARCH and heteroscedasticity is performed by regressing squared residuals on lagged squared residuals or the squared fitted value respectively Otherwise the test variable s are added to the conditional variance model as regressors The test variables are designated regressors of Type 3 if a MA GMA component is selected and of Type 2 if a AR or FI GAR or FIGARCH component is selected an
205. s of one or more variables highlight them in the list and click the Data Graphics button on the toolbar 11 VARIABLE TYPES Explanatory variables in an equation can be of two or three different Types with a different radio button assigned to each In some models typing is irrelevant in which case just choose Type 1 but it has a number of common uses In linear regressions it is used to allow lags to be treated differently Lags up to a specified order can be included automatically so that lagged values do not need to be created and stored individually in the database The number of lags is selected with the scroll bar for all variables of the given Type For example assign non lagged variables such as dummies to Type 1 and distributed lag regressors to Type 2 To allow easy inclusion of the lagged dependent variable the dependent variable in a regression can be assigned as a Type 2 regressor with lags specified The current value is omitted from the regressor set automatically This also works in system models such as VARs In the Dynamic Equation dialog typing regressors in combination with specifying autoregressive and moving average components has a special additional role allowing an equation to feature structural dynamics and or error dynamics See the relevant Help pages and the TSM main document for details on this 12 PARAMETER VALUES A special feature of TSM is the Values dialogs where values and conditio
206. sample selected for estimation will be truncated accordingly The excess observations are not discarded however The end start of the data matrix is extended with missing observations represented by NaN Zs NaN is returned in the case of illegal values e g negative arguments of log and 4 1 2 x lt 0 and x gt Cin log odds 41 James Davidson 2008 3 The Power transformation returns the power of the absolute value for noninteger exponents The square root transformation is an alternative way to take the power of 1 2 but behaves differently assigning NaN to negative observations 4 The symbols and are used in the new variable names to denote multiplication and division in variable names The more logical choices and cannot be used in file names 5 Fourier Transform computes the FFT of the selected series The real and imaginary parts of the transform are vectorized to give a real series of the same length of the original with cosine and sine terms alternating The components can be separated again if required using Edit Shape Note The series as generated are of length 2T and are trimmed to fit the existing data set To avoid losing these points first extend the data set using Edit Re Size Sample 3 3 Setup Model Manager A model is the complete set of specifications values and results from estimation or simulation of an equation or system of equations At any time the program holds in mem
207. se opening a field will automatically insert the variable name and ready for the rest of the formula to be typed OX CODING See Appendix C of the main document for information on compiling supplied code into the program Supplied Ox code can be used to return five types of object according to the selection made with the radio buttons Residuals Return a vector matrix of equation residuals as a function of data and parameters from UserEquation Return solved values and forecasts from UserSolve Log likelihood Return a vector of log likelihood contributions as a function of data and parameters from UserLikelihood Statistic Return a statistic or vector of statistics as a function of data and optional constants passed as parameters from UserStatistic Data Generation Return a generated data set as a function of existing data and constants passed as parameters from UserGenerate Test Only Choose this setting if the only coded function to be returned is 71 James Davidson 2008 Notes a test statistic from UserTest based on the regular estimation outputs selected with the Test checkbox If this option is set the Coded Function checkbox is automatically deselected If the coded functions have been set up for selection by name as described in Appendix C they can be selected in the dialog using the Previous and Next buttons to navigate the list Preset names cannot be edited If no naming funct
208. selected by a checkbox If both this and explanatory variables are omitted the dominant regime depends on the sign of z_t The second set of parameters is unavailable unless Double Transition is checked The number of regimes is fixed at 2 for the ST model If the type of switching selected changed from either explained switching or smooth transition the variable selections for those options are cancelled The option Estimate Regime Differences selects the parameterization that allows individual significance tests of differences between the regimes However note that in a test for no differences between regimes test for number of regimes the switching probabilities or ST parameters are unidentified under the null hypothesis This is a well known testing pitfall and the standard tests don t apply If Estimate Regime Differences is selected with Markov or Hamilton switching then rows 2 M of the Markov transition matrix are likewise expressed as differences from row 1 This allows a test of the hypothesis that transition probabilities are independent of the current regime Analytic forecasts are not available for ST models in this release Use the Monte Carlo forecast option Analytic forecasts are available for the Markov switching models However the number of calculations needed to compute the multi step forecast 2 standard error bands increases exponentially with the number of steps and can become excessive Standard e
209. sistent HAC covariance estimator Set the desired kernel and bandwidth in Options Test and Diagnostics Options 59 James Davidson 2008 14 The SSW LS estimator includes leads and lags of the differences of all variables included as Type 1 regressors The coefficients of these ancillary regressors are not reported in the output Lagging Type 1 regressors is disabled Type 2 regressors can be included with lags chosen by the user not chosen automatically For valid application of the method the dependent variable and Type 1 regressors must all be 111 while the Type 2 variables must all be I 0 stationary 15 The ADF test and the SSW LS estimator depend respectively on a choice of lag length and of lead lag length The lengths L can be selected in two ways a Automatically by optimizing a model selection criterion over the interval 0 lt L lt n 1 3 The selection criterion is is set in Options Test and Diagnostics It is the Schwarz IC by default s Manually using the lag selection scrollbar To enable this option set the model selection criterion to None in Options Test and Diagnostics 16 FMLS and SSW LS cannot both be selected at once Uncheck to latter to select the former 4 2 Model Dynamic Equation This dialog sets up the specifications for a dynamic model As well as setting the basic ARIMA and ARFIMA specifications as specified in equation 3 1 of the main document it also specifies
210. ssian homoscedastic residuals showing generalized autocorrelation Optionally see the checkbox the Model method will always be used for one off simulations and Monte Carlo experiments This setting allows the specification of a Monte Carlo experiment where the bootstrap is used for tests without the need to set up different for data generation and estimation The wild bootstrap variants are not available for Monte Carlo forecasts If these options are selected the regular bootstrap is substituted The random number seed is an arbitrary set of decimal digits If set to 0 default the actual seed will be generated by the system clock and every run will be different Otherwise the seed entered here will be used to initialize random number generation for each Monte Carlo forecast and stochastic simulation The setting Shock Variance is available for Gaussian shocks only If 0 is entered in the text field then the sample variance from the most recent estimation is substituted If this value is zero as if no estimation has been run in the current session then 1 is substituted The block bootstrap option is to allow valid bootstrap inference in mis specified models with autocorrelated errors provided the autocorrelation is not too persistent The chosen block length value is shown as a power of the current sample size When ML Model is selected the parameters of the shock distribution are those shown in the Values Condition
211. ssion methods also return a Hausman type test for the presence of bias Davidson and Sibbertsen 2006 48 O James Davidson 2008 Notes 1 To run the estimation select a variable or variables from the list and press Go Multiple selections are permitted and will be computed in succession Alternatively just double click on a variable in the list Ze The series may be either differenced or detrended by regression prior to computing the periodogram Choose option with the radio buttons 3 Press Sample to select the sample for estimation Sample 3 This is stored independently of the sample selection for other program functions but is shared with Nonparametric Regression and can be set in either dialog See Setup Set Sample for details 4 For the GPH bandwidth and trim options and MS Fourier terms the power of T being selected to nearest integer below is shown as a guideline Note that the optimal bandwidth is typically a power of T times a constant factor that may be small The weight here is 1 5 The GPH bandwidth setting is chosen with the scroll bar GPH recommended M O T 1 2 The minimum MSE setting is known to be M O T 4 5 but the bias can be large with this choice Experimentation is recommended to see how sensitive the estimate of d is to the selection 6 The GPH trimming option also omits the lowest frequencies See the relevant literature for guidance on this setting If in doubt keep at 0 7
212. ssive The option Generate Fractional Series as Type I set by default simulates the effect of presample lags by adding a single vector or matrix of Gaussian random variables with the correct covariance 114 O James Davidson 2008 structure Selecting this option ensures that e g bootstrap distributions match the type I case Notes 1 With this option the fractional process must be stationary 1 e d lt 0 5 To simulate a nonstationary process replace d by d 1 and check the option Impose Unit Root in Model Dynamic Equation 2 The option is not available in conjunction with regime switching A type I process is always generated in this case 3 If the Presample data are held fixed in the simulations required in bootstrap and Monte Carlo forecasting estimates or imposed values of the presample shock components must be available The number of these to be included is set in the type I Fractional text box in Options General if the setting is zero the type II process is generated INFERENCE BY RESAMPLING 13 Two methods are implemented for generating confidence intervals and p values by resampling the data rather than by asymptotic criteria The bootstrap simulates the specified model using the TSM simulation engine with randomly drawn artificial disturbances These can be either drawn from a known distribution such as the normal or Student s t or resampled from the empirical distribution of the estimated residu
213. stimators 8 1 Options Output and Retrievals SAVING DATA FILES Iterations before Temp Reduction 10 3 1 Ox Default 0 1 Ox Default 1 Ox Default 0 off Yes 500 5 0 85 10 No Yes No No Yes 12 points No Yes Yes Yes Yes 1 The type of data file saved XLS CSV WKS IN7 DAT or MAT is determined by the extension added to the file name If no extension is added by the user the one selected in this dialog is included automatically However note that the user s choice over rides the selection in this dialog For example if the name is selected from the list of existing files in the file dialog with extension XLS the selection here is ignored if different OUTPUTTING TABLES AND SERIES Ze The following series can be either printed in the results window or esperes to a file The actual data series Y_t a The fitted series Yhat_t followed by the ex post 1 step forecasts 1f specified s The residuals Y_t Yhat_t solving equation 1 for u_t at the estimated parameters followed by ex post 1 step forecast errors 1f specified If conditional heteroscedasticity options are selected also The variance adjusted residuals followed by ex post 1 step adjusted forecast errors 1f specified X The estimated conditional variances followed by ex post 1 step variance forecasts if specified 103 James Davidson 2008 If a smooth transition model specified a
214. stings tsd files so use this command before storing a model to avoid bulky files Tabulation Load Density Plot Loads a previously saved spreadsheet file containing data for generating density plots in the dialog Graphics Stored MC Distributions The file contents are merged with any existing plot data If a loaded plot has an existing name the name is augmented with q Notes 1 Excel xls spreadsheet files are since version 4 12 the default data format for TSM being a common standard that can handle missing values properly 31 O James Davidson 2008 Data can always be read in this format and exported to a different format for editing in an application other than Microsoft Excel if desired Data files may be loaded by the program automatically as when a settings file or a stored model is loaded If the file in question is not found on the stored path other paths known to the program are searched in the following order the path to the current settings file the current data folder the current results folder and the start in folder Messages are printed to show that this has occurred or if the file is not found anywhere This feature makes it possible to transfer a settings file to another system on which the stored paths are inappropriate However since the file found might not be the one intended it is important to check the program messages If data are saved in MAT format the variable names are listed in
215. switching nor with multiple equation models 5 The model optimizing each of the selection criteria Schwarz Hannan Quinn and Akaike is reported following the run 6 4 Actions Automatic Regressor Selection Given a baseline model containing N regressors of one or more Types including current and lagged values of some variables typically this option estimates all the 2 N possible models formed by taking subsets of the full regressor set It then reports the case which optimizes the chosen selection criterion which can be either the Akaike AIC the Schwarz SIC or the Hannan Quinn HQC Notes 1 Optional settings are selected in Setup Automatic Model Selection regressor Types which also features an alternate launch button and Options Tests and Diagnostics selection criterion 2 The program excludes regressors from the baseline specification by turning their Fixed flags on and setting the coefficient values to 0 In other words the baseline specification is not actually changed during the run To use the selected model for further work it must be specified manually in the usual way If the baseline specification includes regression parameters that are already Fixed this setting is retained and the variable in question is excluded from the search 3 The procedure optimizes exhaustively over the model space looking at every case and hence it is path independent and does not depend on test outcomes Thus it is
216. tart up unless renewed can occasionally occur 141 James Davidson 2008 31 32 33 If you cannot figure out what the problem is reset the program to defaults with File Settings New Alternatively close the program delete the settings tsm file and restart Another option is to write the current settings to a text file File Settings Save Text and inspect this output Note that only non default settings are listed The usage of variable names can be checked in the programming manual If the program attempts to execute an illegal Ox instruction and crashes a message is displayed and then it automatically restarts The Ox error message appears in the console window second TSM icon on the taskbar and can be copied to the clipboard and saved follow the onscreen instructions This message can guide users in debugging supplied code If the error is due to a TSM bug please send in the error message as requested The error recovery screen displays options for quitting continuing and exporting the current settings to a file This file contains valuable diagnostic information preserving the last recorded state of the program before the crash If possible please send in this file along with the error message 142 James Davidson 2008
217. te This could be an ARMA or a regression model for example In the Select Estimator panel choose Gaussian ML Click on Conditional Variance Model The Conditional Variance dialog box opens i Select the GAR and GMA orders id To see the model in the form usually reported the Bollerslev form open the Options ML and Dynamics dialog box and under GARCH Settings uncheck the first two checkboxes Note the model you fit is identical in either case Only the interpretation of the coefficients is affected by these options Press the Go or Running Man buttons to estimate Estimation of GARCH models can sometimes be tricky Poor starting values can cause convergence failure See Help Hints and Tips for advice on optimization in case of difficulty 17 James Davidson 2008 1 User Interface 1 1 The Menus Clicking on most menu items opens a dialog in which program settings can be changed As many dialogs as desired can be open simultaneously Notes The File menu controls loading and saving of settings data and results The Setup menu controls basic operations such as choice of sample size data transformations and storing and loading models It contains dialogs to control special estimation routines such as multiple ARMA models and recursions for preliminary data analyses including summary statistics nonparametric and log periodogram regression and cointegration tests Monte Carlo experiments are also launch
218. te entries on a line with a space and terminate each line with Enter Save the file with extension mat or txt Next select either File Data Open or File Data Merge as appropriate The new variable s are named Var by default where denotes the column number s Give new names using Rename and optionally enter descriptions using Description in the Setup Data Transformation and Editing dialog Before doing anything else save the data in text or a spreadsheet format MAINTAINING AND EXPORTING PROGRAM SETTINGS 15 16 17 To save a model specification including data file name estimator sample size parameter values test options etc open the Model Manager double M button select Store Current Model and supply a name the current run number is the default This facility allows you to work on different projects in parallel during a session You may have a complex multi equation model set up and need to do some exploratory regressions or swap data sets Saving the model allows you to reload the settings later with Actions Load Model and pick up where you left off Your stored models are saved with the other settings in the settings tsm file To keep a permanent copy of your favourite operational settings save them in a backup file with a name such as mydefaults tsm If you then need to change the settings for a particular run they are easily restored by the command File Settings Open and sel
219. test applied to the squared residuals and forecast errors This is asymptotically N 0 1 as both periods tend to infinity This is called Forecast Test 2 If it is desired to compute this statistic for the linear regression case simply open the Dynamic Equation dialog and select Actions Evaluate at Current Values MULTI_STEP FORECAST METHOD 8 9 10 Two methods of computing forecasts and associated standard error bands are provided The analytic method computes formulae for the mean and standard error of the forecast and the plots show two standard error bands corresponding to 95 confidence bands when the errors are Gaussian Lagged dependent variables entering through the AR or fractional model components in the Dynamic Equation dialog are replaced by forecast values to yield a true multi step forecast However please note that lagged dependent variables included as Typed regressors in the Linear Regression dialog for example are not substituted in this way True multi step forecasts are not computed for this case The Monte Carlo method uses the fitted model to compute stochastic simulations of the process and reports quantiles of the empirical distribution for each step In this case all models including those containing lagged 110 James Davidson 2008 11 12 13 14 dependent variables as regressors are computed by dynamic simulation Hence true multi step forecasts are reported in this case Two t
220. th a model are stored in a file with the name of the model and the suffix tsd These files are not intended to be read or manipulated outside TSM To save results to spreadsheet files use the commands under File Listings However note that the latter data cannot be read back into the program for purposes such as graphing or calculating tests If the Store Current Model command is given following a Monte Carlo experiment the replications or frequency tables whichever have been specified are stored in the tsd file under the given model title If the Store Data with Model box is checked a copy of the data set is saved in the tsd file This will be loaded automatically when the model is re loaded If this box is not checked you are prompted to save the current data file if it has been edited and the file with this name is reloaded with the model however there is no protection against it being altered in the interim in this case If Store Results with Model is checked the text of the last run estimation output is stored as a string When the model is re loaded the next tile Actions Evaluate at Current Values is chosen or Calculator button pressed causes a choice box appears presenting the option of re displaying the results If the Save as Generic Model checkbox is checked the data file is not 43 James Davidson 2008 10 reloaded with the model which is the default action This setting is appropriate f
221. the current model residuals 2 Create model for simulation in one of three ways estimate a model retrieve a stored model or type parameter values direct into the Values dialogs 3 A dependent variable or variables must be selected to act as a placeholder and provide any start up values This can be a dummy such as Zeros see the Make Zeros option in Setup Data Transformations and Editing In this case all pre sample lags would be set to zero but chosen presample values could be entered using the Edit command in Setup Data Transformations and Editing 4 To bypass the discard save prompts assign this command to one of the two user selectable toolbar buttons see Options General When the button is pressed most recent choices are applied automatically Use the menu command to change them 5 To simulate without a data set loaded first use the Extend Sample option in Setup Data Transformations and Editing to specify the sample size required Then create a placeholder variable using Make Zeros 6 If estimation is by least squares or GMM the residual variance is not in the parameter set and is estimated extraneously from the residuals If simulation follows estimation the current estimate is used To specify a model for simulation without prior estimation select one of the conditional maximum likelihood time domain estimators This will allow all the model parameters including the error variance to be enter
222. the dialog or the Equation choice widget on the tool bar to switch between them 2 At least one of the parameters in this dialog must be fixed at a non zero value the normalized variable If none is specified manually the first entry is automatically fixed at 1 when the equation is run 5 3 Values Distribution This dialog shows parameters defining the distribution that are not associated with any one equation in a multi equation model These are the Student t parameters degrees of freedom and skewness parameter of the GED distribution parameter of the negative binomial distributions error correlations Parameters of the DCC multivariate GARCH model X Notes 1 In regime switching models use the Next Regime button to cycle through the regimes or Regimes choice widget on the tool bar to select a regime directly 2 Covariance parameters of the BEKK multivariate GARCH model while not associated with any one equation are nonetheless displayed in the Values Conditional Variance dialog See Help page 5 2 for correct interpretation of these parameters 5 4 Values Switching Regimes This dialog displays parameters specified in the Model Regime Switching dialog ES In the Markov switching case including Hamilton s model these are the transition probabilities p_ Ji PGli forming a M M 1 matrix These are the probabilities of switching from regime i to regime j In the Explained Switching
223. the results window Ox cannot read or save a data file containing only zeros See the caveats on artificial data creation using Extend Sample in Setup Data Transformation and Editing When the Clear command is given all menu items and toolbar buttons that operate on data are disabled The purpose of this command is to allow new data to be created or entered in the Setup Data Transformation and Editing dialog The name of a variable which for convenience should not exceed about 20 characters can be extended by a longer description When preparing the data file e g in Excel optionally divide the name field by the symbol E All characters following the form the description Descriptions can be viewed by the command Help Data Descriptions and edited in Setup Data Transformations and Editing see Descriptions The divider character can be changed during installation by editing the file tsmgui4 h and setting the function Get_NameCharacter MISSING OBSERVATIONS Ls The input file may have missing observations e g blank cells in an Excel file and these are replaced in the data matrix by NaN Not a Number If the variable in question is included in a model the sample period is automatically truncated as necessary to exclude NaN observations PERIODIC OBSERVATIONS AND DATES 8 If provided date information years quarters months etc is used to label graphs and printouts and is presented in the Setup Set
224. ti core processor When the run is completed the results are sent to a text file that can be loaded in the TSM window using the command File Load Text File The temporary ox file created to run the job is deleted at closedown if Delete Temporary Files on Exit is checked in Options General If the checkbox Defer External Jobs is checked in Options General the Ox file containing the job is created but not run Use this option if the job is to be run on a different machine for example ADDITIONAL OPTIONS 27 28 The results of the experiment including tables and plots data are automatically stored with the Data Generation model at the end of the run Reloading this model allows the tables using the Results command and graphics to be re displayed at any time When performing a sequence of experiments save the Data Generation model under a new name before modifying it so as to preserve these results for future study The complete set of replications or the frequency table if this option is selected can be also exported to a spreadsheet file for further analysis Give the command File Listings Save Monte Carlo Replications The distributions can also by displayed graphically The command Graphics Monte Carlo Distributions opens a dialog to select and display the empirical densities of each parameter test statistic and p value These are optionally displayed in both histogram and kernel density form The norma
225. ting in the Multi Series plot option in Graphics Show Data Graphic If a multi series graph is plotted by selecting One Graph under Multiple Series Display in this dialog the line styles are used in order starting with 1 Un graphics are drawn using line styles 1 4 Style 1 is used for the main series in each plot including the Actual series in Actual Fitted plots e Style 2 is used for Fitted series Style 3 is used for forecasts Style 4 is used for confidence bands If multiple equation series are plotted in a single graph the line styles are incremented by two or three so as to cycle through the available styles The symbol option Fill does not draw a symbol but shades the region between the line and the zero axis using either light gray in colour plots or a hatching pattern in monochrome plots This option is used by default in the display of probability and conditional variance series Uncheck the checkbox to use the Line Style 1 for these series The Band Fill line style is a special option to indicate regimes or time periods depending on the value of the selected variable It displays light gray bands in those periods when the variable is positive NOTE Band Fill can only be selected for Line 8 Attempting to select it for Lines 1 7 produces a warning message The option Plot Zero Axis is selected by default The zero axis in a plot is drawn as a light grey broken line When the option Scale on Right
226. tional 82 James Davidson 2008 17 18 19 parameters checked here will be added to the test set To compute a Wald test of linear restrictions Rb c or impose these restrictions in estimation the number of restrictions and the elements of c must first be entered in the Model Constraints dialog Then refresh the Values dialog and enter the columns of R 1 e the rows of R transposed in the fields displayed A restriction can involve any subset of model parameters and hence can be spread over two or more number of Values dialogs It may be helpful to open the relevant dialogs together and arrange them on the screen in a column Restrictions may also be applied across equations and across regimes Since only one equation regime Values dialog can be displayed at a time use the choice widgets or Next buttons to switch quickly between them For each linear restriction one parameter must be designated to be solved as a function of the remainder Make this choice by checking the relevant Constrained Wald test checkbox There must be same number of checks in this column as restrictions otherwise an error message is generated It is also the user s responsibility to be sure that the restrictions can be solved uniquely for the checked parameters in other words the square submatrix of R defined by the checked rows must be nonsingular If this property does not hold an error message is generated 5 1 Values Equat
227. to calculate p values for 1 tailed tests Just cut and paste the test statistic into the Look Up Tail Probability dialog Change its sign for tests of the lower tail Select EDF from File then press Select to choose a test statistic from the currently open EDF file the file dialog opens automatically if no EDF file is currently open To open a different EDF file use the command File Data Load EDF The density plot is the same in either dialog The shaded region is the area corresponding to the tail probability and equivalently the area to the right of the critical value 55 James Davidson 2008 4 Model 4 0 Model General The special model features specified in these dialogs conditional variance supplied function regime switching equilibrium relations parameter constraints are turned on and off by checking unchecking the relevant boxes in the main Dynamic Equation dialog The current settings are retained even when the feature is deselected and can be re activated by checking it again The current selection is shown by check marks against the menu items as well as by the check boxes All dialogs are closed before an estimation is run Restore them to their original positions by the Actions Restore Dialogs command or by clicking the Windows button on the tool bar Alternatively select the option to have them restored automatically see Options General BUTTONS Le The Values button either o
228. to remove any unwanted series Xt t 1 T denotes a highlighted variable in the data set Mt t 1 T denotes the marked variable if any j represents the scrollbar setting for leads lags differences C d E represent values entered in the text field Lag Xt j Lead Xt j Difference y Xt Xt Log Difference log Xt log Xt j Difference 100 Xt Xt J Xt j Fractional Difference Sum i 0 t 1 Bi Xt i where Bi Gamma i d Gamma d Gamma i 1 Cumulate E Sum j 0 t 1 Xt j Logarithm log Xt Exponential exp Xt Logistic f exp Xt 1 exp Xt Log Odds f log Xt C Xt C 1 or 100 Square Xt 2 Square Root f Xt 1 2 Reciprocal 1 Xt Power f X E E an integer IXtI E otherwise Sine A sin Pi C Xt Cosine gt cos Pi C Xt Absolute Value IXtl Max X C C Marked max Xt C max Xt C Mt Min X C C Marked min Xt C min Xt C Mt Sign a 1 if Xt gt 0 1 otherwise Add C C Marked Xt C Xt C Mt Subtract C C Marked Xt C Xt C Mt Multiply by C C Marked Xt C Xt C Mt Divide by C C Marked Xt C Xt C Mt Centre Mean Devs Xt Mean X Standardize f f Xt Mean X SD X Detrend z Xt a b t by regression Fourier Transform See 5 below Additional Notes 1 When leads lags are created the
229. to use this technique routinely to impose e g positivity and stability constraints on lag polynomials The search algorithm should usually work OK without this The method is implemented more as a last resort for difficult cases GRID PLOTS 13 14 If bounds are set and the Fixed box is also checked the bounds will be used as the limits of a Grid Plot Either one or two parameters can enter the grid If the Fixed box is checked and both bounds are 0 then the parameter in question is simply held fixed when the grid is drawn If three or more parameter are both fixed and have bounds set the first two encountered are the plotted parameters The others are just treated as fixed in the usual way The number of grid points must be set in the Options Optimization and Run dialog The number is counted from zero Thus if the bounds are O and 1 and it is desired to evaluate at intervals of width 0 1 enter 10 in this text field The likelihood will then be evaluated at 11 points 0 0 1 0 2 1 WALD TESTS AND LINEAR RESTRICTIONS 15 16 To compute a Wald test of joint significance enable Wald Tests in the Model Linear Regression dialog or Parameter Constraints in the Model Dynamic Equation dialog Then check the checkboxes of the variables to be included in the test If the option to test joint significance of the regressors is selected these are included automatically and do not need to be checked her Any addi
230. ts box must be checked Wald tests can also be performed separately see Actions Compute Test Statistics Wald Test SYSTEMS OF EQUATIONS 25 26 Select system estimation by checking the System of Equations checkbox When a system of equations is specified the estimator computed depends on the estimator selection If the option LGV FIML is selected the log determinant of the error covariance matrix is minimized Least Generalized Variance or FIML in the simultaneous equations case see 22 below In these cases the covariance parameters are concentrated out and do not appear in the vector of parameters If the option ITV 2SLS GMM 3SLS is selected the estimation method is system GMM with the instruments selected If the estimation is launched with the Actions Run Estimation commands or the Run button the error covariance matrix set equal to the identity matrix However if the command Actions Multi Stage GMM is given twice in succession the second run uses the efficient weights matrix estimated from the current residuals This iteration 64 James Davidson 2008 can be repeated as often as desired The form of the weights matrix used depends on the Covariance Matrix Formula setting see Options Tests and Diagnostics either standard robust allowing for heteroscedasticity or HAC a If the Gaussian ML Student t ML or GED ML estimation options are selected the error variances and contemporaneous co
231. uch simpler to implement a Save and use tabulations of test EDFs This feature implements size correction and estimation of true test powers in simulation experiments Can also be used to make bespoke tabulations of non standard tests Save Selected command write selected variables from data set to new file Harris McCabe Leybourne HML test for long memory of data residuals Two assignable toolbar buttons other interface improvements Improved implementation of supplied Ox coded statistics Fourier bootstrap option Nyblom Hansen model stability tests XK XX XA XX TSM 4 18 Code recompiled under Ox 4 02 Dedicated Stop button on toolbar to pause calculations Data plots can be displayed directly by clicking the variable list in any dialog and then the Chart button Excel dates for weekly and daily data are read with the data and used in the output and plots TSM 4 17 Progress indicator for numerical optimizations shows the number of iterations and current criterion value Improved code for setting model specifications Parameter values and settings are now preserved under deletion restoration of regressors In systems equations can be deleted restored without losing values and settings Enhanced Monte Carlo module allows multiple experiments in a single run Experiments can also be extended with additional replications User supplied statistic option allows the Monte Carlo module to have a fully general ap
232. ugh this introduction before starting work with TSM It does not aim to describe all the capabilities of the package These can best be discovered by browsing the menus in conjunction with the Help pages provided for each Its purpose is to outline TSM s unique design and operating conventions to first time users KKK K K K K K K K K K K K K K Working with TSM KKK K K K K K K K K K K K K K 1 ENTERING DATA Regression packages often have their own proprietary database formats and getting data into them from different sources can be troublesome By contrast TSM reads either ASCII files or spreadsheet files directly It works smoothly in conjunction with popular spreadsheet programs such as Microsoft Excel Lotus 123 and OxMetrics for preliminary data organization and for further analysis and graphing of outputs It can itself merge datasets with different start and finish dates and use and display date information including daily dates in Excel format It offers flexible single observation editing series transformations and dummy creation capabilities 2 MENUS AND DIALOGS TSM is operated in Graphical User Interface GUI mode by setting the options in a number of dialogs These can be opened from the menu bar or by shortcut buttons on the tool bar Some operations can be performed in several different ways For example an estimation run can be launched from the menus from the Running Man toolbar button and also from the Go buttons i
233. uired Notes l Giving any other estimation command for example Actions Run Estimation or the Run button resets the program so that the next Actions Multi Stage GMM command yields Stage 1 again Zi It may be possible to iterate the procedure to convergence so that no further change in the estimates occurs However this procedure does not optimize the GMM criterion function 3 This option is not available for IV estimation from the Model Linear Regression dialog 6 8 Actions Compute Test Statistic Opens a sub menu listing test options ll Score LM Test x Moment M or CM Test Wald Test of Set Restrictions Specified Diagnostic Tests Bootstrap Test of I 0 Notes 1 By default the statistics printed by selecting these options are asymptotically Chi squared with degrees of freedom indicated in parentheses The nominal p values of the tests are shown enclosed in braces following the statistic values Ze The option of printing the F form of the tests with associated p values from the F tabulation can be selected with the checkboxes in the relevant dialogs Note In most cases the F form is to provide an alternative approximation to the asymptotic Chi squared distribution These tests are exact only in special cases SCORE LM TEST 3 This option opens a dialog to allow specification of a test of the significance 90 O James Davidson 2008 of additional regressors selected from the data set Rad
234. user for the current run is therefore the user who starts the program User editable Ox file used to start the program incorporating the user s own code The program can be started by running this file in OxEdit See Appendix A on changing module settings This is the standard container for user s Ox code although it is often convenient to have it contain just include compiler directives referring to files of code supplied by the user Written by TSM4 at startup and deleted at closedown Used to signal an error termination Named settings file with tsm extension same format as settings tsm saved by the user Can be loaded manually to overwrite existing settings When created using the File Export option data and listings are bundled with the settings The corresponding files are recreated automatically when the file is loaded in this case The program creates various files in standard text format 134 James Davidson 2008 xls csv tsd OX plt png eps including results files images of the results window text and settings files created with the Settings Save Text command These files can be view and edited in Windows Notepad or other word processing programs Microsoft Excel spreadsheet format is the default format for saving data sets forecasts and other listings Other options available in the Options Output and Retrieval dialog csv files are text files have the sam
235. utomatically However provided the parameter sets match the models can otherwise be different In particular parameters can be fixed in the estimated model to values different from the DGM such as 0 This option allows the analysis of omitted variable bias for example Any optional tests that are specified in the estimation model will be included in the tabulations The routinely computed diagnostic tests Jarque Bera test and Q tests can be optionally included in the tabulations By default they are omitted The upper tail quantiles of the distributions of the test statistics 50 10 5 2 5 1 are optionally reported in the case of parameter t values By default the absolute t values are tabulated so that for example the 5 tail quantile should be approximately 1 96 in large samples when the null hypothesis is true Also optionally reported are the empirical distribution function EDF points for the nominal p values If the test criteria are correctly sized these distributions should be Uniform 0 1 if the null hypothesis is true and 100x of replications should lie below x Over rejection yields a value larger than the nominal one The cases tabulated are x 0 01 0 025 0 05 0 1 0 5 Optionally the signed t statistics can be tabulated instead of the absolute t statistics to allow the evaluation of one tailed tests In this case the 5 tail quantiles should be approximately 1 64 in large samples when the null hypot
236. y the function value itself lagged j periods E without a lag is replaced by 0 In systems of equations the names E 1 j E 2 j denote the values for each equation The variable names Z and z are reserved for used in nonlinear ECMs and are replaced by the values of the equilibrium relation In models with two or more equilibrium relations use Z 1 Z 2 to denote the values 25 James Davidson 2008 2 File 2 0 File General Information This menu gives access to submenus for Settings gt gt Save and load tsm files Data gt gt Save and load data files including empirical distributions for test statistics Results gt gt Control the saving to a file of output from the results window Listings gt gt Save items of output from estimation or simulation runs to spreadsheet files Graphics gt gt Save a copy of the most recently displayed graphic Load Text File Allows the results window to be used as a text editor The contents of the chosen file will be appended to the existing window contents Save Selected Text Allows any part of the text in the results window to be saved to a file Give this command after highlighting the desired text by dragging with the mouse The options presented are to append the text to the current results file and to write to overwrite a new existing named file Restart gt gt These options close the program saving all settings and optionally data and immed
237. ype Criterion 3D Plot Type Density Options Histogram Normal Curve CDF Colour Monochrome Keep PLT files Extended Actual Fitted Fill Probs and Var plots Line Width Symbol Size ML and Dynamic Options E AE AA F BF A RR Maximum ARMA GARCH Order MA Polynomial with s Root of Student t d f Log of Skewness Parameter Restrict Pre Sample Lags GARCH coefficients in Standard Font Type 2 GARCH intercept Root of GARCH Intercept No Gauss Seidel Its in GARCH M GARCH M Trimming Factor A Compute EGARCH Likelihood by G S No G S Its to compute EGARCH Optimization and Run Options x Report Minimand 102 0 system clock 1 Fixed No Yes No Once Equal Tails 99 No No No 50 PNG No Yes YYYY 640x480 Bands One Frame Lines Both Yes No No Colour James Davidson 2008 No Grid Points for Criterion Plot A Absolute bound on dynamic params Max No of BFGS Iterations Iteration Print Frequency Strong Convergence Crit Weak Convergence Crit Parameter Rescaling Factor Simulated Annealing SA Iterations Initial Temperature Temperature Reduction Factor XA EX E AX E General Options Restore Dialogs Automatically Enable Savings Prompts Store Model After Each Run Delete Temporary Files on Exit Automatically Close Options Dialogs Size of Results Window Text Echo Results to Console Show Tool Tips Enable Error Recovery Drag Selection Enable Optimization E
238. ypes of Monte Carlo plot are available Time plots show the median and 2 5 and 97 5 percentiles so that the plotted bands in this case show a true 95 confidence interval neglecting estimation error even when the disturbances are non Gaussian Alternatively kernel densities can be displayed for the complete empirical distribution of any forecast step Analytic standard error bands for regime switching models use a recursive algorithm involving m K function calls for M regimes and K steps ahead In Hamilton s model the number of effective regimes is M number of lags Unless they converge rapidly these calculations can become very time consuming They are therefore terminated automatically after 100 seconds has elapsed Unless the bands have converged sufficiently to be extrapolated thereafter only the point forecasts are reported for the remaining steps NB diminishing returns set in rapidly Even raising this factor substantially could yield at most a couple of extra steps The display mode for standard error confidence bands including omitting them can be selected in Graphics Options In dated daily weekly data it is not possible to plot forecasts with date information beyond the end of the observed sample since the information is missing An error message is displayed In this case either change the date type to No Dates or extend the data set and supply the additional dates manually This must be done outside TSM MO

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