Home

Demetra+ User Manual - CROS

1. tems list contains variables chosen in ListSele ctor panel Tae On the right the list of all user defined regression variables is displayed The user can select variables that will be used as calendar regressors with buttons in the middle of the ListSelector panel DEMETRA User Demetra User Manual final version4 doc 54 DEMETRA User Manual Example Easter effect Specifications 12Doc 1 AICC Difference Transtormation E Trading days Calendar effects Type Predefined n Regression Fretest True Arima modelling Detalls in use True Remove Pretest Pretest the significance of the easter regiesson valab statistics for w 1 8 15 E D iaaa Comments a agama a spec Pre specified regression variables User defined outliers are used if prior outliers knowledge suggest that such effects exist at known time points e Additive Outlier AO additive point outlier which occurred in a given date f It is modeled by variable fort t AO O fort t e Level shift LS variable for a constant level shift beginning on the given date ft It is modeled by regression variable l fort lt t is f O for t2 t e Temporary changet TC variable for a temporary level change beginning on the given datef It is 9 Definitions from X12 ARIMA Reference Manual 2007 10 In TramoSeats method this type of outlier is sometimes called by transitory change
2. a set of measures of the quality of seasonal adjustment The quality diagnostic implemented in original seasonal adjustment algorithms are different for each SA method Moreover their interpretation could be problematic for an unsophisticated user For this reason in Demetra the qualitative indicator was build in Indicator s values are described in the following table Meaning of the quality indicator2 Vawe Meaning failure in the computation of the test etc Error There is a logical error in the results for instance it contains aberrant values or some numerical constraints are not fulfilled The processing should be rejected for serious quality reasons no actual error and the results can be used The result of the test shows that the quality of the seasonal adjustment is uncertain The result of the test is good from the aspect of the quality of seasonal 26 The model also contain a flag Accepted which simply means that the user decided to accept the results no matter what are the different diagnostics DEMETRA User Demetra User Manual final version4 doc 87 DEMETRA User Manual adjustment Several qualitative indicators can be combined following the basic rules Given a set of n diagnostics the sum of the results is Bad Undefined All diagnostics are Undefined There is at least 1 Error There is at least 1 Severe diagnostic but no error A No Error no Severe diagnostics t
3. T O Excel O ODBC Folder d sarepository iw Presentation List E i Stringi Array y String Collection Editor Enter the strings in the collection one per line f Caw matrix eres For example the following collection f D y DEMETRA User Demetra User Manual final version4 doc 43 DEMETRA User Manual will generate all the forecasts all the D tables of X11 and the series yc yl The different files will be stored as follows lt folder gt lt workspace name gt lt processing name gt _ lt code gt csv where e lt folder gt is specified by the user or the temporary folder if unspecified e lt workspace name gt is the workspace name can be omitted e lt processing name gt is the name of the multi processing e lt code gt has been defined above It should be noted that for multi processing that don t belong to a workspace the lt workspace name gt lt processing name gt sequence is replaced by demetra 3 3 X12 Doc This item is visible in the application s menu when X12 seasonal adjustment has been previously executed and after that it has been activated by the user 12Do0c 1 Specification Current specification Copy Faste Lock Add to workspace The option Current specification opens specification that is currently displayed in the central application panel The user can modify the specification and validate changes using the Apply button Demetra re estimates the
4. 60 From TramoSeats structure it can be shown that estimator will always underestimate the component The amount of the underestimation depends n the particular model as a rule the relative underestimation will be large when the variance of the component is relatively small MARAVALL A 1995 61 The theoretical variance Estimator should be similar to the estimate actually obtained Estimate Large differences between the theoretical and empirical values would indicate misspecification of the overall model MARAVALL A 1995 DEMETRA User Demetra User Manual final version4 doc 138 DEMETRA User Manual seasonal lag If the model is correct the empirical estimate of autocorrelation function should be close to the theoretical estimator autocorrelation function For i th component the discrepancy between ACF function of the components and of the estimator can be substantial for small values of innovation variance Var a If the components derived from the time series vary with stability the distortion in the ACF of the components induced by estimation is stronger for the more stable with low Var a one It means that these distortions are large when components have a low importance For ACF functions Demetra presents the following tables trend fs fomo fonsa oos oon a C E e e fomo oos oos osses e fomo oo joome oo ao in fone joze ps ao fomo foom foon posa e fomo foom oos ossa e fomo
5. DEMETRA User Demetra User Manual final version4 doc 55 DEMETRA User Manual X12 Comments Individual Argument spec modeled by regression variable TC eens amp fort 2 ty where is a rate of decay back to the previous level 0 lt amp lt 1 Seasonal outliers are not supported Pre specified outliers are simple forms of intervention variables Ramps regression variables Ramp effect means a linear increase or decrease in the level of the series over a specified time interval f to It is modeled by regression variable l fort St RP t t t t 1 fort lt t lt t 0 fort2t All dates of the ramps must occur within the time series Ramps can overlap other ramps additive and level shifts outliers Intervention regression variables No corresponding X12 arguments The variables intervention variables are defined as in Tramo Following the definition these effects are special events known a priori strikes devaluations political evens and so on Intervention variables are modeled as any possible sequence of ones and zeros on which some operators may be applied The most frequently used operators are e Dummy variables e Any possible sequence of ones and Zeros l 0 lt 6 lt 1 1 B POE 1 B ee ee 1 B U B These operations enable to generate not only AO Ls TC and RP outliers but also sophisticated intervention variables that are well adjusted to the p
6. Mode Undefined Use forecasts True Regressi E 1 General LSigma 1 5 lt USigma 2 5 Estimati Seasonal filter oe Lee i Details on seasonal filters Automatic henderson filter True HE Seasonal filters Ioj x JE i SS Ss ESS es pp Choose the filter for each penod m w Mer eam 4 2 TramoSeats specifications TramoSeats specification is based on the original program taking into account that peripheral specifications or specifications related to diagnostics are handled in a different way The different parts of the specification are presented in order in which they are displayed in the graphical interface of Demetra Details on the links between each item and its corresponding X12 spec argument are provided in the following paragraphs For an exact description of the different parameters the user should refer to the documentation of the original TramoSeats program DEMETRA User Demetra User Manual final version4 doc 66 DEMETRA User Manual 1 General description oe Meaning parameters Transformation Arima Model Transformation of the original series Others Calendar effects Others Specification of the part of the regression related to TradingDay Easter calendar Effect Regression Others ireg Specification of the part of the regression which is not specifically related to calendar Automatic modelling Others Automatic model identification automatic model ident
7. DEMETRA User Demetra User Manual final version4 doc 105 DEMETRA User Manual SA sal Seasonally adjusted series without regression effects Sho Sati S O TOR itd f Trading days effects SSS MHE mb _f Moving holidays effects w o eeens O ooo RMDE Ramadaneffects S OMHE i Other moving holidays effects _ OTOT out _ Outliers effects Olcmp T 5 1 out_t out_s out REGTOT reg _f REG cmp Y SA reg_y _f T S I reg_sa _f Other regression effects reg_t _t reg s _f reg_i _f DET cmp T S IY det _f det_y _f det_sa _f Deterministic effects det_t _f det_s _f det_i _f For those components in additive case the following relationships should be true MHE EE RMDE OMHE 1 CAL TDE MHE 2 OTOT OT OS 0OI 3 REGTOT REGT REGS REGI REGY 4 REGSA REGT REGI 4 DET CAL OTOT REGTOT 5 CT T OT REGT 6 CS CAL OS REGS 7 Cl I OI REGI 8 CSA Y CS CT CI REGY 9 Y CT CS CI REGY T S I1 DET 10 DEMETRA User Demetra User Manual final version4 doc 106 DEMETRA User Manual Y Y DET T S I 11 SA Y S T I 12 SEVT ESF 13 A multiplicative model is obtained in the same way by replacing the operations and by and respectively The Definition test verifies that all the definition constraints are well respected The maximum of the absolute differences is computed for the different equations and related to the Euclidean norm of the init
8. jae j E 2000 2006 01 01 2007 02 01 Parameter of the regular filter that can be applied on the sequences of ones Lancet ok _ Example User defined variables RegVa rProperties DEMETRA User Demetra User Manual final version4 doc 58 DEMETRA User Manual 4 1 6 Automatic modelling X12 Comments Individual spec IsEnabled Presence or not of the automdl individual Spec Accept default automdl acceptdefault Controls weather the default model is chosen if the Ljung Box Q statistics for its model residuals is acceptable Check Mu automdl checkmu Controls weather the automatic model selection procedure will check for the significance of a constant term automdl mixed Controls weather Arima models with m nonseasonal AR and MA terms will be considered in the automodel Ljung Box Q statistic Balanced automdl balanced Controls weather the automatic model procedure will have a preference for balanced model HR initial automdl hrinitial Control weather MHannan Rissanen 13 estimation is done before exact maximum likelihood estimation to provide initial values limit in the automatic differencing procedure Final unit root automdl Threshold value for the final unit root test in limit the automatic differencing procedure This value should be greater than one ArmaLimit automdl armalimit Threshold value for t statistics of Ar
9. 0 01 1999 01 2000 01 2001 01 2002 01 2003 01 2004 01 2005 01 2006 01 2007 01 2008 01 2009 Abnormal values 88 1 Breakdowns of unstable factors and Average Maximum Differences across spans 7 00 Distribution 6 00 5 00 4 00 3 00 2 00 1 00 0 00 0 200 400 600 800 1000 DEMETRA User Demetra User Manual final version4 doc 123 DEMETRA User Manual Model stability E Main results H Fre processing Reg rima H Decomposition X11 Diagnostics Seasonality tests fe Spectral analysis H Revisions history H Sliding spans The diagnostics output window provides some purely descriptive features to analyze the stability of some parts of the model like trading days Easter and Arima Model stability analysis calculates Arima parameters and coefficients of the regressors for different periods and visualizes these results on the graphics The parameters of the model chosen for the complete time span are computed on a moving window The length of the window is 8 years The points displayed on the figure correspond to the successive estimations The figures are helpful for assessing about the stability of the model parameters On the picture below the results of model stability diagnostic for trading days Easter and Arima model are shown e trading days parameters stability 0 01 5 e 0 005 0 01 0 015 a 0 02 Monday Tuesday Wednesday Thursday Friday Saturday Sunday DEMETRA User Demetra
10. 01 2007 01 2006 01 2006 r oe oF 01 2009 01 2010 01 1991 01 1993 01 1992 01 1994 01 1995 01 1997 01 1996 01 1999 01 1998 01 2001 01 2000 01 2003 01 2002 01 2004 01 2005 01 2007 01 2006 01 2008 01 2009 01 2010 Table presents the original series with forecasts and forecast error the final seasonally adjusted series the final trend with forecasts the final seasonal component with forecasts and the final irregular component in the following way 1 1931 2 1991 1991 4 1991 51991 6 1991 7 1991 1941 931 10 19_ 11 142 1132 Original senes 2618 10104 10712 12695 Final seasonally adjusted senes 9920 93 10504 2 107914 11744 124737 124344 117594 10648 2 122474 10784 9 111652 11762 6 10273 3 10736 7 11152 11555 11856 5 11962 118820 8 11687 5 11483 3 113059 7 11153 9 10945 1 Final trend compone Final seasonal 074352 1 661698 0 731099 0 699392 0 680827 0 209336 0 852499 0 993241 1 13701 2 63208 Final irregula C Fi 0 9657 0 97a344 0 967662 1 01635 1 05206 1 0395 0 369783 0 917081 1 06654 0 953596 1 00101 1 07463 Final trend component forec The table can be copied to Excel by dragging and dropping the top left corner cell to excel sheet DEMETRA User Demetra User Manual final version4 doc 91 er 0 5 B g Anal D B U ESSE Px AS Ee ri r18 82 8 72 1 BG 43 76 6 76 8 7
11. 12 R5A3 Concurent Valid IMPORTS CIF 12 RSA5c Concurrent Valid definition Good 0 000 annual totals Good 0 000 MES H Spectral seas peaks Good spectral td peaks Good reganma residuals normality Good 0 234 independence Good 0 262 spectral td peaks Uncertain 0 030 spectral seas peaks Uncertain 0 013 Unemployment 5A series 01 7199501 199601 199701 1996 01 199901 2000 01 200101 2002 01 200301 200401 200501 200601 2007 01 200601 200901 201001 2011 New processing 7items 1 1 0 0 1 1 ao 2 tc i Is 2 The processing is actually launched by means of the Run command under the SAProcessing 1 main menu item SAProcessing 3 Rt WOO at reports Edit Priority Add to workspace Initial order The user can also launch the seasonal adjustment of the time series by clicking on its name on the list 2 Creation of a multi processing via wizard When the user activates the wizard the empty window is displayed The wizard guides the user through the construction of the associations series specifications It also gives him the possibility to define and to use specifications that don t belong to the workspace Consecutive steps are similar to those which were described in single seasonal adjustment part However there are two main differences First of all in the first panel the user can choose more than one time series and
12. For seasonally and trading days adjusted series the following statistic is being calculated 97 FINDLEY D F MONSELL B C BELL W R OTTO M C and CHEN B C 1998 98 X 12 Arima Reference Manual 2007 99 FINDLEY D F MONSELL B C BELL W R OTTO M C and CHEN B C 1990 DEMETRA User Demetra User Manual final version4 doc 198 DEMETRA User Manual De j max A min A j min A where The index j ranges over all spans containing month t The value A is considered to be unreliable if it is higher than 0 03 If both period t and t belobgs to at least two spans the seasonally adjusted period to period 100 4A A _ T are marked as unstable if100 percentage changes t 1 j j max A _ min gt 0 03 J A J J 1 1 Where A k the seasonally or trading day adjusted value from span k for month t N1 t k period t and t 1 are inthe k th span The index j ranges over all spans containing month t 12A Tests Doornik Hansen test is defined as follows let s skweness k kurtosis of the n non missing residuals We make the following transformations Transformation of the skewness D Agostino E 3 n 27n 70 n 1 n4 3 n 2 nt 5 n 7 n 9 w 1 2 B 1 p 100 X 12 Arima Reference Manual 2007 DEMETRA User Demetra User Manual final version4 doc 199 DEMETRA User Manual 1 J0 5log 1
13. oma oo oes 62 MARAVALL A 1993 DEMETRA User Demetra User Manual final version4 doc 139 DEMETRA User Manual transitory a C E E s fomo oo ozn O oss e fomo mos oos oe SS e fomo oos oosa ora e fomo mo oos O oons irregular ao ooo o oon oos oreas O s fomo oom ona pora O e oom oon ea ors zo fomo ooon oos oser eo pen oms fome pers P values of this test are given in the last column of each autocorrelation table The user should check whether the autocorrelation exist or not special attention should be given to first and or seasonal order autocorrelation Th The coefficients of the autocorrelation function of the irregular component are always null in the Component column while are not null in the Estimator column It is because the irregular component is a white noise however its final theoretical estimator usually has a moving average structure Meaning of the p value for autocorrelation tests Value PS Meoning YO Good no evidence for autocorrelation Uncertain a mild evidence for autocorrelation Bad strong evidence for autocorrelation 63 MARAVALL A 2000 DEMETRA User Demetra User Manual final version4 doc 140 DEMETRA User Manual It should be stressed that this test gives no information about the direction of autocorrelation Comparison of the theoretical MMSE estimators with the estimates actually calculated can be used as a diagnostic t
14. 0 731528 0 699143 0 948077 0 880188 0 809065 0 824548 0 991832 1 136479 632977 9916 368 10498 27 10747 64 11737 07 12478 14 12440 98 11767 94 10651 8 12253 98 10800 21 11170 46 11761 RA olf After choosing odbc option the user should specify database source name DSN Needless to say this database should be previously created The user defines the components that will be sent to the database DEMETRA User Demetra User Manual final version4 doc 42 DEMETRA User Manual Save onginal series Save calendar effects Save sa seres Save seasonal component Save trend Save iregular component Save model CSV By using the csv format it is possible to save for multi processing documents a large number of time series generated by the models For all the series of the processing each file contains a specific output for instance the calendar effects of all the series will be put together in one file The different files will contain one item row or column for every series in the processing even if that item is empty The software can generate different layouts the series can be presented in the form of horizontal or vertical tables each row column corresponding to the same period or in the more compact form of horizontal lists of data The series must be introduced in the String Collection Editor one code by row The user can also use wildcards in the usual way to identify the series Txt seres
15. Accepted Series Method Estimation Processing Priority Quality Sold production of industry TS RSAS Concurrent Valid 0 Severe CPI CA petite TS RSA5 Concurrent Valid 0 CRUD Faste TS RSA5 Concument Valid 0 EXPO Cut X12 R5 Concument Valid 5 MPOR X12 R5 Concurrent Valid 10 MPOR Copy AV2 RS Concurrent Valid 10 Linemp TS Interactive Valid 0 IMFO ee XIRS Concurrent Valid Priority Method Run Refresh Accept For X12 method it is possible to assign different seasonal filter to each period using option Mixed in specification window It is done in a two step procedure First the time series should be seasonally adjusted using the same seasonal filter for every period Once seasonal adjustment has been executed the user is able to modify settings for seasonal filter and change the filter that will be used for estimating seasonal component for each period To do it Seasonal filter should be set to Mixed then the user chooses Details on seasonal filter Finally the user should specify seasonal filter for each period DEMETRA User Demetra User Manual final version4 doc 166 DEMETRA User Manual HE X12 RSA5c Industries alimentaires 001563038 Apply Restore Save H Main results Eevee RegArnme Basic Transtommation Calendar Sepan TEE Auto Modelling Enabled Arima Outliers Mode Undefined FE Seasonal filters Use forecasts True LSigma 15 USigma 2 5 Seasonal fiter Mixed Details on
16. EXPORTS FOB a IMPORTS CIF om IMPORTS CIF ine IMPORT UNIT VALUES IMPORT PRICES Right click on any time series name opens the pop up menu which contains the following commands Add Remove Clear Add opens new time series set from the Excel workbook Remove removes all time series from the workbook The button is active only if the name of the workbook is marked It is not possible to remove all workbooks at the same time Clear cleans the browsers window Xml Excel Tsw usce JE k E Remove 2 Clear If the user wants to put the workbook into cash memory one should activate the star next to the Excel s workbook name The list in the Star menu contains all workbooks which are currently in the cash memory DEMETRA User Demetra User Manual final version4 doc 17 DEMETRA User Manual Xml Excel Tsw usce DATADORD2 xls Insee xls Using the Tool icon see below one can remove marked item or clear the window The Simplify tree option collapsed tree with opened branches Xml Excel Tsw usce Remove Clear Simplify tree EAPORTS EAPORTS FROREH IMPORTS CIF IMPORTS CHIH FH Demetra reads files written for TSW The TSW folder can contain several levels of sub folders with TSW files They will appear in the tree navigator of the TSW provider The series in a subfolder will be grouped in a collection called All series The same idea was applied for USCB sou
17. Easter corrections 0 0 00 Last section Matrix view panel provides information similar to the matrix output of TSW TramoSeats for Windows program The summary information is divided into five folds available in the right side of the panel e Main contains main statistical properties of the Arima model used in Pre processing e Calendar presents calendar specification results e Outliers outlier structure of each series and coefficients of Arima model and their significance levels e Arima parameters values and their t stat values e Tests p values of different tests computed on the residuals and with other information annual discrepancies between raw and adjusted data spectral visual peaks Main Matrix view panel is presented below DEMETRA User Demetra User Manual final version4 doc 162 DEMETRA User Manual l0 x Processing Summary Matrie view l BP BD BQ S amp fres O val El Reports Series N log mu a 1 0 1 1 0 128 21 066 D EXPORTS FOB 630 1 0 1 IMPORTS CIFT 630 1 0 1 IMPORTS CIFT 630 1 0 1 0 1 1 0 115 40 257 0 1 1 0 114 30 568 ie a a m fs gt of G w The matrices can be copied by the usual keys combination Ctrl C and used in other software like Excel 4 4 2 2 Multi processing menu Menu offers the following options for multi processing Run runs the defined multi processing seasonal adjustment Update reports upd
18. User Manual final version4 doc 99 Residuals DEMETRA User Manual The way in which Demetra calculates the residuals is presented in the Annex section 1A Residuals from the model are presented in the graph and in the table 0 1 0 05 al 0 0 05 Full residuals 01 1992 01 1994 01 1996 01 1998 01 2000 01 2002 01 2004 01 2006 01 2008 01 201 jan feb mar apr may jun jul aug sep oct nov dec 1991 0046 0 009 0 005 O00 0022 0035 0019 OO 0007 0006 0024 0 020 1992 0004 0018 0002 O007 OfO16 OFf14 0005 0030 0001 0 005 0 008 0 024 1993 0040 0 0270 0028 0024 0008 0 011 0 006 00027 0008 0008 0020 0 029 1994 0014 0012 0 016 0 028 0 031 0 006 0006 0005 0007 0012 0 004 0 019 1995 0 028 0 011 0012 O08 0002 0005 0007 0006 0073 O01 0009 0016 1996 0009 0005 0015 0002 0003 0006 00144 0029 0011 0010 0009 0 015 1997 0 007 0009 0010 0037 0002 0014 0012 0011 0016 0031 0 029 0 015 1998 0 017 0 023 0022 0004 0015 00065 0028 0024 0015 0011 0004 0 007 1999 0013 0005 0000 0 028 0019 0006 0 000 0005 0002 0036 0012 0 016 2000 0 006 0 022 0006 0000 O07 0024 0001 0027 0007 00299 0018 002 2001 0 0273 0 008 0000 0021 0 011 0 006 0 003 0013 0 001 0042 0 021 0 013 Analysis of the residuals consists of several tests which are described in the Annex section 12A Summary statistics are presented in the following tables 1 No ty of the residuals
19. ae O B T O B Let B F V B F os E B F Bi B E b F Fi which are called PsiE weights As it can be seen the PsiE weights are obtained from the Wiener O B Kolmogorow filter by multiplying by 6 B Hence PsiE weights can be divided into two components first one see Base Bene applies to prior and concurrent innovations second one are D 4 B applies to 92 MARAVALL A 2008 DEMETRA User Demetra User Manual final version4 doc 189 DEMETRA User Manual to s while future i e posterior to t innovations a determines contribution of a _ j J A determines contribution of a to Sr For j 2 0 PsiE weight j determines contribution of total innovation from period T j to component estimator xi For j lt 0 PsiE weight j determines contribution of total innovation A from period 7 j to component estimator xi It is assumed that T gt 20 1 Hence estimator of the seasonal component can be expressed as si E BY a E FY ap B a is an effect of starting conditions present and past innovations in series while F a is an effect of future innovations which is a zero mean convergent one sided stationary MA process e Errors analysis For each i th component total error in the preliminary estimator d arag IS expressed as A M Mitit k d itlt k where m i th component A M the estimator
20. i l N zz s k X je X e the inter year sum of squares i N 2 gt Xi X ie Xej X e the residual sum of squares i l Un aw M II l DEMETRA User Demetra User Manual final version4 doc 203 DEMETRA User Manual The null hypothesis H is that b b b which means that there is no change in seasonality over the years This hypothesis is verified by the following test statistics n I k 1 which follows a F distribution with k 1 and n k degrees of freedom e Test for presence of identifiable seasonality This test combines the values of the F statistic of parametric test for stable seasonality and the values of the moving seasonality test which was described above The test statistic is Where F is a stable seasonality test statistic and F is moving seasonality test statistic The detailed test s description is available in LOTHIAN J and MORRY M 1978 e Combined seasonality test This test combines the Kruskal Wallis test along with test for the presence of seasonality assuming Stability evaluative seasonality test and test for presence of identifiable seasonality All those tests are calculated using the final unmodified S I component The main purpose of the combined seasonality test is to check whether the seasonality of the series is identifiable For example identification of the seasonal pattern is problematic if the process is
21. 17 5667 2008 ass 2 fose ae m oa anay ooo Ba as foem 7 a 1398 1190 12 zoss os osz E od September 2640 E 0 282 sd 0 566 ss 0 509 od DEMETRA User Demetra User Manual final version4 doc 118 DEMETRA User Manual Sliding spans Main results Pre processing RegArima Decomposition 411 Diagnostics Seasonality tests H Spectral analysis H Revisions history be SA seres changes E Model stability It is expected that seasonally adjusted data are stable which means that removing or adding data points at either end of the series does not change the SA results very much The sliding spans analysis checks the stability of seasonal adjustment outcome It is also used to detect the timing significant changes in the time original time series Such changes include seasonal brakes and large number of outliers and fast moving seasonality The sliding spans analysis is particularly useful in case of seasonal brakes 9 large number of outliers and fast moving seasonality A span is a range of data between two dates The sliding spans are series of two three or four depending on the length of the original time series seasonal moving averages used only for X12 method and series frequency overlapping spans The program sets up a maximum of 4 spans The spans start in 1 year intervals The sliding spans analysis stands for the comparison of the correlated seasonal adjustments of a given obser
22. 205 TramoSeats Monitor ts_monitor executes the processing DEMETRA User Manual new TramoSeats Monitor TramoSeats TramoSeatsResults ts_rslts ts_monitor Process s ts_spec j x12 specification equivalent RSA5 full automatic X12 Specification x_spec XK12 Specification RSA5 launches tramo seats core engine X12 Monitor x_monitor new X12 Monitor executes the processing X12 X12Results x_rslts x_monitor Process s x spec seasonally adjusted series TSData ts_sa ts_rslts Series SAComponentType CSA TSData x_sa x_rslts Series SAComponentType CSA computes diffrences between both results TSData diff ts_sa x_sa IT comp tes Statistics on the DescriptiveStatistics stats double max stats Max min diff Length differences new DescriptiveStatistics diff Values stats Min rmse Math Sgrt stats SumSquare more advanced uses computed on the fly Periodogram periodogram new Periodogram x_rslts X11lResults DTables D8 Values roots of the moving average polynomial of the arima model used by Seats Complex roots ts_rslts Seats SArima MA Roots DEMETRA User Demetra User Manual final version4 doc 206 DEMETRA User Manual REFERENCES ANSLEY C F 1979 An algorithm for the exact likelihood of a mixed auto regressive moving average process Biometrika 66 59 65 BOX G E P and TIAO G C 1975 Intervention Ana
23. 61 74326 59 74658 3 74654 52 7526366 192359 07 7359748 f4417 05 5621 69 T5681 04 78728 63 140425 8 139384 1 141692 2 144931 6 148012 8 151700 6 154747 6 160454 2 162408 5 165037 170176 5 173413 4 179602 4 178239 7 160850 5 183236 3 185907 5 191080 2 M3 23563 8686 2205213 23513 54 2459124 25613 43 25934 04 26635 17 27641 01 27907 99 27630 6 21663 32 2769436 21255 87 2646r r8 21403 8685 21286 09 20034 44 20060 73 Time series are identified by their names Demetra derives information like data periodicity starting and ending period from the first column After they have been marked and copied in Excel the data can be integrated in Demetra as follows Select the Xml panel in the browsers 5 Refer to Chapter 3 5 for detailed description of this functionality DEMETRA User Demetra User Manual final version4 doc 14 DEMETRA User Manual e Paste the data they appear in the tree This option doesn t work if some files were previously opened via Xml browsers In this case select the button New first and then Paste e Change the names of the series collection in the tree if necessary click twice on the item you would like to modify e Save the file if need be Demetra is compatible with Excel 2003 and Excel 2007 2 2 Browsers The browsers panel presents the series available in the software Different time series providers are considered Xml specific sc
24. Do oa X 0 o 0 a Oo DO opo00000000000d0 o o 0 4 o J5 0 2 0 D P2 Plo 5 10 15 20 25 30 35 Tramo model regular AR 1 0 84816 B 0 63239 B 2 0 27735 B 3 seasonal AR 1 regular MA 1 seasonal MA 1 0 85116 5 Frequency of the regular AR roots 3 14159265358979 1 7652530287 34H Frequency of AR roots is useful for detecting a stochastic trading days effect or stationary seasonality As it is shown in the picture below Demetra highlights such values in the output red color and warning DEMETRA User Demetra User Manual final version4 doc 133 DEMETRA User Manual 1 1 0 8 0 5 0 6 0 4880859000868 ogoo00000000000000m o oo 0 4 o 05 5 0 2 n 4 0 Pili Pl 5 10 15 20 25 30 35 Tramo model Polynomials regular AR 1 0 31167 B 0 18514 B 2 0 10083 B 3 seasonal AR 1 regular MA 1 seasonal MA 1 0 637615 Frequency of the regular AR roots 3 141592765358979 1 04669433030803 Seasonal frequency seats model Polynomials regular AR 1 0 2675 B 0 15759 B 2 0 12744 B 3 seasonal AR 1 regular MA 1 seasonal MA 1 Frequency of the regular AR roots 3 14159765358979 1 042227 752219647 Seasonal frequency Regressors and Residuals Regressors section presents all deterministic regressors used in Tramo part including trading days variables leap year effect Easter effect outliers ramps intervention variables and other user defined variables In the next part the residuals which
25. Henderson moving average Seasonal fiter 3 x 5 moving average DEMETRA User Demetra User Manual final version4 doc 102 DEMETRA User Manual TBH 336 2183 38 05 The M statistics are used to asses the quality of seasonal adjustment 2 These statistics vary between 0 and 3 but only values smaller than 1 are acceptable M1 measures the contribution of the irregular component to the total variance M2 which is very similar to M1 is calculated on the basis of the contribution of the irregular component to the stationary portion of the variance Statistic M3 compares the irregular to the trend cycle taken from a preliminary estimate of the seasonally adjusted series because if this ratio is too large it is difficult to separate the two components from each other Statistic M4 tests the randomness of the irregular component The Statistic M5 is used to compare the significance of changes in trend with that in the irregular Statistic M6 checks the S I seasonal irregular component ratio because if annual changes in the irregular component are too small in relation to the annual changes in the seasonal component the 3x5 seasonal filter used for the estimation of the seasonal component is not flexible enough to follow the seasonal movement It should be underlined that statistic M6 is calculated only if this filter has been applied in the model Statistic M7 is the combined test for the presence of identifiable seasonality The test compares the
26. NA 183 6A Initial values for Arima model CStiMatiOn ccccccccccssssseeeccccccecsaeesseeececeessaaasseceseesauaeasess 191 TA Cancellationot AR and WIA Ta CONS aivcoceinssaceccnheenswinssececateauenes E 191 SA XAL tapena TE seats ta neti sataeaasteaes nn T tae ange er one een 191 OR SPET aa Wolsssteseta later ean acces paesa taut sence taahicce E 194 10A SREVISIONMMISCORIES posaran ic inca eomendaaatansics dav avaaucaavmnaa nave nuanasennes A 197 TIA SIGNS Pan tseiee nck te uteo Suh o2 seh a tans hese an eat aeiee aes eee aaah ore 198 NZI THC SUS i ricetaleetiasca se nhcaceue Aedes eee re tees aati ena ae eae ee ee eek 199 13A Code to generate simple seasonal adjustments CH ou cecccccceeesccessecsseeeeseseeeeeseseeeeeseeees 205 REFERENCE Siona A E A 207 DEMETRA User Demetra User Manual final version4 doc 6 DEMETRA User Manual Introduction Seasonal adjustment SA is an important step of the official statistics business architecture and harmonisation of practices Since the 1990s Eurostat has been playing a leading role in the promotion development and maintenance of an open source software solution for seasonal adjustment in line with established best practices Developed by Eurostat Demetra software was intended to provide a convenient and flexible tool for seasonal adjustment using TramoSeats and X 12 Arima2 methods In 2008 the European Statistical System ESS guidelines on seasonal adjustment have been endorse
27. User Manual final version4 doc 38 DEMETRA User Manual Browsers Demetra can load data from the following data sources e Excel XCLPRVDR e ODBC Open Database Connectivity a standard software interface for accessing database management systems e SDMxX Statistical Data and Metadata eXchange a ISO standard for exchanging and sharing statistical data and metadata among organizations e TSW denotes TRAMO SEATS for Windows the seasonal adjustment software developed by the Bank of Spain e USCB denotes X 12 Arima the seasonal adjustment software maintained by the U S Census Bureau e Xml Extensible Markup Language designed to describe data e Txt With default settings the xml Excel TSW and USCB sources are available The user can add remove data sources with option sEnabled The order of the data sources visible in the Browsers window can be arranged with Position function the source with the smallest position value is displayed on the left in the Browsers panel paes _ _ i x see at all WorkSpace jon 21 De aU Stepeacessing oulpu z Rine Browsers Cables XCLPRVDA Fosti ODBCPRVDR ESE TSW USCB ae Txt DEMETRA User Demetra User Manual final version4 doc 39 DEMETRA User Manual Formatters For XML and TXT data sources Demetra offers formatting options like switching between vertical and horizontal presentation of the data showing dates and titl
28. X11 Series span gt series Span data interval of the available time selection type series used for the processing The span can be computed dynamically on the series for instance Last 90 obs Pre processing z Transformation O Series spar gt Calendar effects Selection type 2 Regression E Arima modelling gt Outliers detection 2 Estimation Decomposition 411 3 sn Comments a nn spec Transformation transform function Demetra accepts the following options None data are not transformed Log logarithms from original values are taken Auto Demetra tests which option None or Log is better for the particular time series AIC ee aicdiff Disabled when the transformation is not set to Auto a E adjust Acceptable values e LeapYear include a contrast variable for leap year LengthofPeriod include length of month or length of quarter as a regression variable DEMETRA User Demetra User Manual final version4 doc 50 DEMETRA User Manual Transformation Transformation AIC Difference Calendar effects Regression E Arima modelling Leap r ear Qutliers detection LengthofPeriod gt Estimation Decomposition 211 Adjust Preadiustment of the series for length of period or leap year effects The seres is divided by the specified effect Not avaiable with the 4 Calendar effects faerie AICC Difference regressio
29. allowed to create any fix day regression variable Example predefined trading days AICC Difference 0 E Trading days Calendar effects Type Predetined Regression Pretest True E Arima modelling E Details Outliers detection Trading days TdNoLpYear gt E stimation Length of period None i Decomposition 11 El Easter effect In Use ls enabled Type Type of regression varables DEMETRA User Demetra User Manual final version4 doc 53 DEMETRA User Manual Example calendar trading days Specifications X12Doc 1 AICC Difference Transtormation El Trading days Calendar effects Type Calendar Regression Pretest True Arima modelling El Details iw Automatic modellin Trading days Td Length of period None Holidays to seb Holidays Specific holidays Example user defined trading days This option is available if the user has created user defined variables see 3 1 2 First user defined regression variables must be specified see 3 1 2 BF Variables Name Type Freq Start End Description Var_1 Static 12 1 2000 2007 varl Var_2 Static 12 1 2000 2007 var2 Ver_3 Static 12 1 2000 5 2007 vers Var_4 atic Tz 1 2000 2007 vard X125pec 1 a m x Basic AICO Difference 0 a Transfonmation O Trading days in use Calendar effects e UserDefined Regression Pretest True E Aima modeling E Details Outliers detection E hems 2 items Estimation 0 Var_1 Decomposition X11 1 Var_3 x
30. and then choose the button on the left hand side as it is shown on the picture above Then put the parameter value using decimal point if necessary and mark Fixed option ParametersEditor ioj x Unstable polynomial Choose other values 16 The unstable estimate means that slight changes in input data lead to large changes in estimates This situation takes place if estimates are highly correlated DEMETRA User Demetra User Manual final version4 doc 61 DEMETRA User Manual The example below shows the Arima 2 1 1 0 1 1 model specified by the user For phi 1 theta 1 and btheta 1 the user introduced the initial values Moreover phi 1 and theta 1 values are fixed It is not compulsory to specify initial values for all parameters If the user changes the Arima parameters for active processing the model will be re estimating and results will be updating after using Apply button ParametersEditor loj x p Basic Transformation gt Calendar effects a Regression Arima modelling z Automatic modelling e Outliers detection Estimation i Decomposition X11 0 6700 rr rr TSt 0 1812 0 0627 0 0043 0 6700 OOO o S 0 0625 0 0004 For fixed parameters standard error T Stat and P value are not computed 4 1 8 Outliers detection False 2 0 6708 1 1 40 6708 Both X12 and TramoSeats detect outliers which are defined as the abrupt changes that cannot be explained by the u
31. are obtained after estimation of Arima model in Tramo are presented both in the graph and the table Analysis of the residuals consists of several tests and residuals distribution DEMETRA User Demetra User Manual final version4 doc 134 DEMETRA User Manual 4 3 2 2 3 Decomposition Main results Pre processing Trama Seats Decomposition fe Stochastic series Model based tests E WK analysis H Diagnostics Seats receives from Tramo the linearized series original series corrected for the deterministic effects and missing observations The decomposition made by Seats assumes that all components in time series trend seasonal and irregular are orthogonal and could be expressed by Arima model Identification of the components requires that only irregular components include noise Each model is presented in closed form i e using the backshift operator B In the main page of Decomposition Seats the following items are presented e Model Arima model for the series e Trend Arima model for the trend component of the series e Seasonal Arima model for the seasonal component of the series e Transitory Arima model for the transitory component of the series e Irregular Arima model for the irregular component of the series The trend cycle component captures the low frequency variation of the series and displays a spectral peak at frequency O On the contrary the seasonal component captures the s
32. are of finite order A white noise variable is normally identically and independently distributed with a zero mean and variance of the component _ innovation the variance of the 1 period ahead forecast error of the component V a Two different components don t share the same unit autoregressive roots The components can be also expressed in compact form 46 For definition of innovations refer to the Annex section 5A 47 Orthogonality means that behavior of each component is independent from other components In particular causes of seasonal fluctuations are independent from causes of long term evolution of the series 48 Trend means trend cycle 49 It is assumed that irregular component is a white noise variable which means that it follows ARIMA 0 0 0 0 0 0 model DEMETRA User Demetra User Manual final version4 doc 128 DEMETRA User Manual 0 B x 6 B a where Q B is a product of the stationary and the non stationary autoregressive polynomials Seats decomposition fulfills the canonical property that is it maximizes the variance of the irregular component providing trend seasonal and transitory as stable as possible in accordance with the models For each component the value of innovation variance is represented through the ratio of the component innovation variance V a to the component Arima model to variance of the series innovation V a gt t k Var a Var a k represents th
33. be put forward for short series non decomposable models Seats or when the differenced series doesn t show seasonal peaks Information on those warnings is displayed by a tooltip on the series The user can sort the multi processing by clicking a column header The example is shown below Serie Method Estimation Processing Priority BUSINESS CONFIDENC X123 R5 BUSINESS CONFIDENC X12 R5 Concurent Valid BUSINESS CONFIDENC X12 R5 Concurrent Valid BUSINESS CONFIDENC X12 R5 Concurrent Valid BUSINESS CONFIDENC X12 R5 Concurrent Valid BUSINESS CONFIDENC X12 R5 Concurrent Valid BUSINESS a tao aig va DEMETRA User Demetra User Manual final version4 doc 160 DEMETRA User Manual By clicking on the time series name a summary of the tests results is displayed in the right panel For the description of those tests refer to Chapter 4 3 2 1 At the bottom of the window the graph of final seasonally adjusted series and raw series is displayed EE SAProcessing 1 E _ Oj x Series Method Estimation Processing Priority Quality Warnings Computed Unemployment TS R5A3 Concurrent Valid Sold production of industry TS RSA3 Concurrent CPI CAPITAL CITY TS RSA5 Concurent Valid CRUDE PETROLEUM P TS RSA5 Concurrent EXPORTS FOB Al2 RSA3 Concurent Valid IMPORTS CIF1 AlA RSAI Concurrent Valid IMPORTS CIF1 Ala RSASc annual totals Good 0 000 x SM spectral seas peaks Good s
34. de Trabajo Np 1116 Banco de Espana MARAVALL A and PIERCE D A 1986 A Prototypical Seasonal Adjustment Model Documentos de trabajo Banco de Espana NEWBOLD D and BOS T 1982 On the use of the Hannan Rissannen Criterion in the time series model selection Department of Economics University of Illinois OTTO M C BELL W R and BURMAN J P 1987 An iterative GLS approach to maximum likelihood estimation of regression models with ARIMA errors Research Report No 87 34 Statistical Research Division Bureau of the Census PLANAS C 1998 The analysis of seasonality in economic statistics a survey of recent developments Questiio vol 22 Eurostat SHISHKIN J YOUNG A H and MUSGRAVE J C 1967 The X 11 variant of the Census Method II seasonal adjustment program Technical Paper No 15 U S Bureau of the Census SOKUP R J and FINDLEY D F 1999 On the Spectrum Diagnostics Used by X 12 Arima to Indicate the Presence of Trading Day Effects after Modeling or Adjustment Proceedings of the American Statistical Association Business and Economic Statistics Section 2006 Seasonal Adjustment Filters for Short and Moderate Length Time Series Journal of Official Statistics Vol 22 No 1 http www census gov ts papers findleymartinjosreprint pdf 2007 X 12 ARIMA Reference Manual Time Series Staff Statistical Research Division U S US Burea
35. defined user calendar and user define regressors in calendar module o Easter effect automatically detected or user entered Easter effect o Outliers effect on the irregular component additive and transitory change outliers e Outliers effect on the trend component level shift effects o Total outliers effect the sum of the outliers effects on trend and irregular components o Separate regression effect user defined variable effect assigned to none of components e Regression effect on the trend component ramps intervention variables for which Delta 0 and DeltaS 0 and user defined variable effects assigned to trend Regression effect on the seasonal component intervention variables for which DeltaS 031 and user defined variable assigned to holiday Regression effect on the irregular component user defined variables effects assigned to irregular o Regression effect on the seasonally adjusted series the sum of the regression effects on the trend and irregular components and separate regression effects e Total regression effect the sum of the regression effects on the trend seasonal and irregular components and separate regression effects 31 If both Delta 0 and DeltaS lt 0 intervention variable automatically assigns to seasonal component DEMETRA User Demetra User Manual final version4 doc 98 DEMETRA User Manual Arima This section consists of three parts It demonstrates a t
36. done by using the ARIMA model which is created in the TRAMO phase of seasonal adjustment Then Seats applies the filter to extended series Cleveland and Tiao 1976 Regarding to the importance of final or historical estimators derived applying the WK filters that are bi infinite and symmetric filters Demetra presents several graphics showing their properties see the Annex section 5A The corresponding graphs for components and for final estimators of the components vary as components and final estimators follow different models For example the seasonal component follows the model 0 B s y B a while MMSE estimator of st A seasonal component follows model B s B F a These graphics are listed below e Spectrum of final estimators The shape of the spectrum of the final estimators is shown in the first graph Spectrum of estimator of the seasonal component is obtained by multiplying squared gain of the filter by spectrum of the linearized series From the example below it is clear that these spectra are similar to those of the components although estimator spectra show spectral zeros at the frequencies where the other components have spectral peaks Estimator adapts to the structure of the analyzed series i e the width of the 69 See the Annex section 5A DEMETRA User Demetra User Manual final version4 doc 145 DEMETRA User Manual spectral holes in seasonally adjusted series dark blue
37. drop them into Selection window DEMETRA User Demetra User Manual final version4 doc 158 DEMETRA User Manual Multi processing definition wizard 3 x Choose series Choose the method Pas ss 2 115 13107 12 1 1980 7 2007 oo 115 13109 12 1 1980 7 2007 115 131010 12 1 1980 72007 click the next step 5 115 rror 115 13106 12 z 115 13108 12 115 13109 12 115 131010 12 115 131011 12 115 131012 12 115 131013 12 You have to drag drop series or groups of J Ha staan drag and drop the time series form seres from the available time series providers 115 131015 12 central zone to the right hand area to the selection list i 115 131016 12 115 131017 12 115 131055 12 El Then the user should decide which seasonal adjustment method X12 or TramoSeats will be used After that the user can chose existing specification or create new specification as it was shown in 4 1 and 4 2 Multi processing definition wizard xj Choose series Choose the method Add items z Calendar effects Regression H Arima modelling The specification contains all the necessary parameters to make a seasonal adjustment You may either select a pre defined specification or choose a new specification Function lam None no transformation of data Logstakes logs of data Auto the program tests for the logdev Next in the add items Demetra presents time series which will be a
38. ee Differencing Differencing window gives the access not only to the data presented in chart and table and spectral graphs but also to ACF and PACF functions for selected time series In order to obtain the output the time series from the list should be dragged and dropped precisely into Name box Differencing 98g oe weiBopouey eeg 2000000000 bookmarks m Jub J n rT 2000000000 4000000000 01 1955 01 1965 01 1975 01 1985 01 4995 01 2005 01 1960 01 1970 014 4980 04 4990 01 2000 01 2010 Using the bookmarks on the right the user could switch to other functions like periodogram and auto regressive spectrum autocorrelation function and partial autocorrelation Once the user changes the differencing orders D regular differencing order BD seasonal differencing order or changes the time series the results are updated automatically The user can identify D and BD parameters that generate stationary time series using Estimate button In right button menu standard options like Copy Export Print are available DEMETRA User Demetra User Manual final version4 doc 36 DEMETRA User Manual 3 2 2 4 Options The window contains the default options used by the Demetrat F Fomatters Diagnostics Dutputs The initial settings can be modified by the user The menu includes e setting for workspace e default processing output e settings for the browsers e formatters for txt and
39. effect 07 0 6 05 0 4 03 p 0 2 LJ o go PPPP PORTS 7 G opopogoog 8 0 soseeoseottgostoscoteft FERRE TEES Sf osooesool ge 6000006 4 9 P oroooooog 4 0 1 i i Y a8 oO 0 2 0 3 L The graph below presents WK filter weights for lag 12 i e for the observation x _ where is the last available observation It can be noticed that in this case WK filter uses both observations x 1 2 48 and observations x 7 1 2 12 to calculate t i preliminary component estimator DEMETRA User Demetra User Manual final version4 doc 152 DEMETRA User Manual 07 0 6 0 5 0 4 03 0 2 a 0 1 o a a 0 eoocccocons geeccscenes PESsssesi ge a o k o a ii a 0 1 o a a s 0 2 a e ACGF stationary represents auto correlation functions of the preliminary estimators of the stationary components For the preliminary estimators of the stationary components Demetra calculates ACGF for lag O to 60 The preliminary estimators imply the use of asymmetric filters while when lag 0 the preliminary estimator is the concurrent one and it is obtained with a one sided filter The ACGF profiles of preliminary estimators when lag 60 preliminary estimators approach the final ones x are very close to the profiles of the ACGF of final estimators itlt 60 When the lag approaches 0 they differ more DEMETRA User Demetra User Manual final version4 doc 153 DEMETRA User Ma
40. how to do it This function is omnipresent in Demetrat i e it is the usual way to move information between different components The objects that can be moved e g time series collections of time series can take different forms nodes in trees labels in lists headers in tables lines in charts etc When a drag and drop operation is initiated which means that an object is indeed moveable the cursor of the mouse changes to either a no parking sign or to a sign The second one indicates an acceptable drop zone Time series from Excel can easily be integrated in Demetra The users can import their own data sets The series must be formatted in Excel as follows Empty top left cell A1 True dates in the first copied column Titles of the series in the corresponding cell of the first row Empty cells in the data zone correspond to missing values missing values can appear in the time series except the beginning and at the end of the series This format corresponds with the format used by the Excel browser which also requires the input zone to start at the beginning of the sheet A1 The exemplary file is presented below 31 Dec 96 31 Jan 97 20 Feb 97 31 Mar 97 30 Apr 97 31 May 97 30 Jun 97 31 Jul 97 31 Aug 97 30 Sep 97 31 Oct 97 30 Nov 97 31 Dec 97 31 Jan 96 20 Feb 98 31 Mar 98 30 Apr 98 31 May 98 Currency M1 67865 96 6366053 63625 74 65497 64 6663533 6903324 1672 27 74386
41. in the Annex section 13A Amongst the peripheral services offered by Demetra the following ones should be stressed e Dynamic access to various time series providers Demetra provides modules to handle time series coming from different sources Excel databases through ODBC WEB services files text TSW USCB xml SDMxX the access is dynamic in the sense that time series are automatically refreshed by the software which consults the providers to download new information The model allows asynchronous treatment e Common xml formatting the seasonal adjustment processing can be saved in xml files which could be used to generate for instance WEB services around seasonal adjustment The software was designed to allow the adding of new modules without modifying the core application The main features that can be enriched are listed below e Time series providers the users could add their own modules to download series coming from other databases e Diagnostics on seasonal adjustment e Output of SA processing As mentioned above the API could be used to generate completely independent applications but also to create more easily extensions to the current application Demetra is compatible with Windows XP Windows Vista and Windows 7 Although Demetra is a 32 bits application it also works with 64 bits version of operating system 1 2 Demetra application for Microsoft Excel A Demetra application for Microsoft Exc
42. innovation a rather than on the series x For each component figure below A presents how the contribution of total innovation to component estimator Xi varies in time the size of this contribution is shown in Y axis For observations Q0 X axis PsiE weights show the effect of starting conditions present and past innovations in series while for observations lt 0 they present the effect of future innovations It can be seen that they are non convergent in the past they are convergent when series x is stationary On the contrary the effect of future innovations is a zero mean and convergent process PsiE weights are important to analyse convergence of estimators and revision errors 75 See the Annex section 5A For more information see Maravall 2008 DEMETRA User Demetra User Manual final version4 doc 149 DEMETRA User Manual 0 6 re 0 5 o amp 0 4 ool 0 3 8 o f ao 0 2 doooopoooooopoopopopot pt T 7 Ti 0 1 Lae g 5 a to a a E ey a eo ra 0 HoSooHdhssoodsoooossssdooogedoag MTSI o0oeeBeegs SSBBs Hoods a a o oO o o os 4 i k a a Oo Oo a l z Ol 4 0 1 i e Preliminary estimators H Main results H Pre processing Tramo Decomposition Seats z Stochastic series Model based tests WK analysis e Components e Final estimators Preliminary es Fane EER E Diagnostics In this part different types of g
43. it is expected that gt o Var Component gt Var Estimator O Var Estimator is close to Var Estimate If for a component Var Estimator gt gt Var Estimate then the component is underestimated On the contrary Var Estimator lt lt Var Estimate indicates the overestimation of the component In the last column of the table p values of the second over under estimation tests are provided Green p value means Good yellow means Uncertain and red means Bad If Var Estimator gt Var Estimate for a particular component then O p values in red indicate strong underestimation of the component variance O p values in yellow indicate mild underestimation of the component variance O p values in green indicate no underestimation of the component variance If Var Estimator lt Var Estimate for a particular component then O p values in red indicate strong overestimation of the component variance O p values in yellow indicate mild overestimation of the component variance O p values in green indicate no overestimation of the component variance e Autocorrelation function The autocorrelation function ACF is the basic tool in the time domain analysis of a time series For each component Demetra exhibits autocorrelations of stationary transformation of components estimators and sample estimates They are calculated from the first lag up to the 57 MARAVALL A 2005 58 MARAVALL A 1993 59 MARAVALL A 1997
44. n 1 n 3 A O 12 n 2 z log y 4 y7 1 Transformation of the kurtosis Wilson Hilferty J n 3 n 1 n 15n 4 Pon n 2 n 5 n 7 n 27n 70 60 pa n 7 n 5 n 7 n 2n 5 60 _ n 5 nt Dnt Dn 377 11n 313 l 126 A ar c s s vy 2 k 1 s _ l ip a a if Then the Doornik Hansen test statistic is defined as the sum of squared transformations of the skweness and kurtosis Asymptotically the test statistic follows a chi square distribution DH z 2 2 Liung Box test Ljung Box test is defined as follows let P the sample autocorrelation at rank j of the n residuals The Ljung Box statistics is 2 LB k ne Pi j1t J DEMETRA User Demetra User Manual final version4 doc 200 DEMETRA User Manual If the residuals are random it will be distributed as yv k np where np is the number of hyper parameters of the model from which the residuals are derived Seasonality tests This section presents the set of seasonality tests calculated by Demetra Detailed description of these tests and testing procedure is available in LADIRAY D and QUENNEVILLE B 1999 e Friedman test stable seasonality test Friedman s test is a non parametric method for testing that samples are drawn from the same population or from populations with equal medians In the regression equation the significance of the month or quarter effect is tested Friedman test requires no di
45. n Specifications H E TramoSeats H JE Alz Clone Then new specification appears on the X12 specifications list DEMETRA User Demetra User Manual final version4 doc 85 DEMETRA User Manual X12Spec 4 and X12Spec 5 are identical The user can modify the settings of X12Spec 5 specification by double click on its name and changing parameters in the specification window AIC Diference Trading days Type Pretest E Details Predefined Trading days Length of period C Easter effect ls en All specifications created by the user can be modified at any time 4 3 2 Seasonal adjustment results single processing Once the active specification is chosen the series that will be seasonally adjusted should be double clicked The processing is immediately initiated using the selected specification and the chosen series DEMETRA User Demetra User Manual final version4 doc 86 DEMETRA User Manual Demetra Prototype IV 10 x Workspace Seasonal adjustment TramoSeatsDoc 2 Tools Window Help Browsers Xml Excel Tsw usce PEE A double click on the time series Jr Inseexds 50 i i Series has been log transformed E FRANCE Alim et tabac 11 Diagnostics Trading days effects 6 variables AD Muti processing Industries alimentaires 001563038 No easter effect aa 2 outliers detected IIS Specifications 4a Single processing Pre processing Tramo _ gt TramoS
46. oas n ooz Residual a e Tos oas A Value 105 6788 Distribution F stat with 11 degrees of freedom in the numerator and 179 degrees of freedom in the denominator P Value 0 0000 Seasonality present at the 1 per cent level The test statistic was calculated in the following way 0 3532 12 1 lt F 11 179 S 0 0544 l 191 12 The p value is 0 0000 so the null hypothesis is rejected and it could be assumed that the seasonality in time series is significant e Evolutive seasonality test The test verifies if seasonality is stable over years The test value placed below indicates no evidence of moving seasonality on 20 per cent level Degrees of feedon Mean square 0 0001 0 0002 Value 0 7419 Distribution F stat with 14 degrees of freedom in the numerator and 154 degrees of freedom in the denominator P Value 0 7296 No evidence of moving seasonality at the 20 per cent level The test value was computed in a following way 0 002 1 14 F 0 706 0 0305 154 38 Because sum of squares displayed by Demetrat are rounded rather than exact the result of computation made by the user is not the same as one obtained by Demetrat DEMETRA User Demetra User Manual final version4 doc 112 DEMETRA User Manual e Combined seasonality test Combined seasonality test uses Kruskal Wallis test test for the presence of seasonality assuming stability evaluative seasonality test and
47. removes all time series from the chart Paste pastes time series previously marked Export settings for export the chart the option for chart can be copy to clipboard and save to file is also available Print allows printing the graph and setting the print preview and printing page setup options Legend add removes legend from the chart Kind displays m m or q q and y y growth rates for all time series in the chart previous period and previous year options respectively Settings allows to adjust the chart to the user s preferences the user can change color scheme change a line chart to the bar chart show hide vertical and horizontal axis show hide legend show hide title modify title change to log scale 210 12 00 _ Unemployment 10 00 8 00 6 00 4 00 20 Copy Copy growth data 0 00 Remove 2 00 Copy all Copy all growth data 4 00 Remove all 6 00 Paste a cn a es 11 2005 09 2006 07 2007 05 2008 03 2009 01 2010 11 2010 04 2006 02 2007 12 2007 10 2008 08 2009 06 2010 04 2011 3 2 2 Tool window The Tool window offers the following options TS Properties Chart Growth Chart Seasonal Chart Spectral Analysis and Differencing The first three of these have been described in previous sections The remaining ones are characterised below 3 2 2 1 Seasonal chart Seasonal charts present the final estimation of the seaso
48. select the series D11 from X12 window and drop the series D11 into the same X12 window from which D11 was selected 3 2 1 Container Container includes helpful tools to display the data The following options are available Chart Grid List or Growth Chart Sp Container H 2 Chart F Tool Window Fk El Grid Options List e Growth Chart At first the user should choose one or few containers from menu Workspace Seasonal adjustment Growth Chart Tools Window Help Container A Chart P Tool Window gt E Grid Options ioi x Then the user can take any series or group of series from one of the browsers and drop it in a container DEMETRA User Demetra User Manual final version4 doc 31 DEMETRA User Manual Workspace Seasonal adjustment GrowthChart Tools Window Help cm 21 7761900 IMPORTS CIF CPICAPITALCITY e i i CPI CHANGE CRUDE PETROLEUM d Morocco 4 1219 27 9773 enchants 1 1973 24 8174 it EXPORTS FOB pf oe on IMPORTS CIF 26 1785 8403500 a IMPORTS CIF1 P 26 7862 35362100 INDUSTRIAL PROD MINING PRODUCTIO EXPORTS if EXPORTS FOB e IMPORTS CIF IMPORT UNIT VALUE r m 01 2005 01 2006 01 2007 01 2008 01 2009 01 201 4 b The group cannot be marked using Ctrl button from the keyboard One can add the series to chart or grid by dragging and dropping them one by one Different ser
49. significance is based on the range s s of the s A values where A m s max s A A m s min s A A s A k th value of autoregressive spectrum estimator 96 Definition taken from X 12 Arima Reference Manual DEMETRA User Demetra User Manual final version4 doc 196 DEMETRA User Manual A The particular value is considered to be visually significant if s A at a trading day or seasonal frequency A other than the seasonal frequency A 0 5 must be above the median of the plotted values of s A and must be larger than both neighboring values s J _ and s A by A A at least 6 52 times the range s s For a given series Y 9 7 which may contain missing values the periodogram is computed as follows In a first step the series is standardized Jt O y l l 2m T In a second step we compute at the so called Fourier frequencies OS which are the values of the periodogram 2 N where N is the number of non missing values t lt T 22 t 0 z defined Under the white noise assumption the values of the periodogram should be asymptotically distributed as a Chi square with 2 degrees of freedom The default frequency td for trading days is computed as follows for series of quarterly series tal Other frequencies correspond to trading days frequencies e For monthly series 2 714 default 2 188 e For quarte
50. table below presents that two slinging spans statistic calculated for January have been above 3 and average maximum percent difference across spans for this period was 1 8 Abnormal values 4 3 Breakdowns of unstable factors and Average Maximum Percent Differences across spans Period Breakdowns Average February it March C August september October November 45 FINDLEY D MONSELL B C SHULMAN H B and PUGH M G 1990 DEMETRA User Demetra User Manual final version4 doc 122 DEMETRA User Manual A large number of unstable estimates revealed by the sliding spans analysis supports an idea of changing the model s specification The example of such a situation is presented below Because of the large share of moving seasonality for all spans test statistic is above 4 the test for presence of identifiable seasonality failed see the Annex section 12A for tests descritpion Sliding spans summary Time spans Span 1 from 1 1998 to 11 2006 Span 2 from 1 1999 to 11 2007 Span 3 from 1 2000 to 11 2008 Span 4 from 1 2001 to 11 2009 Tests for seasonality Kruskal Wallis Moving seas identifiable seas Means of seasonal factors CT CY E Fery asos oaaae Josen orl fees foer asr soea Ee E T E E E E oy mos a emn a august faoss foeaos erosa eros October sess Jona mon jono d Noveme fasso faas ozz Jena C December mss ross fesa 0475 2000
51. test for presence of identifiable seasonality in procedure that tests whether the seasonality of the series is identifiable For the time series analyzed in this section combined seasonality test seasonality has been identified Combined test identifiable seasonality present e Residual seasonality test Residual seasonality test is F test computed on seasonally adjusted series on the complete time span and on the last 3 years span Demetra displays here F statistics and conclusion drowned from them No evidence of residual seasonality P values calculated for this test are given in Diagnostic gt Residual seasonality diagnostics part Residual season test No evidence of residual seasonality in the entire series at the 10 per cent level F 0 2132 No evidence of residual seasonality in the last 3 years at the 10 per cent level F 0 3454 Spectral analysis E Main results H Fre processing Reg rima H Decomposition X11 Diagnostics fuae Seasonality tests Residuals i SA seres stationary H Revisions history H Sliding spans l Model stability Demetra provides spectral plots to alert to the presence of remaining seasonal and trading day effects in seasonally adjusted time series The graphics are available for residuals irregular component and seasonally adjusted time series In order to compare the results with spectral analysis for raw time series the user should create the relevant graph for raw time series fr
52. the example below a RSA5c specification has been used and trading days effects have been detected From the table below it can be noticed that the regressor for Saturday influences time series in the opposite direction to the other trading days regressors In spite of the fact that some trading days regressors are insignificant on 5 significance level the outcome of the join F test indicates that the trading days regressors are jointly significant DEMETRA User Demetra User Manual final version4 doc 96 DEMETRA User Manual Calendar effects Trading days Parameter Value Std error 0 558382 Wednesday Friday zd O280201 0632428 Joso 06937 Saturday 0 829103 0 628534 0 1902 Sunday derived 1 04896 0 659838 Join F Test on trading days F 4 1350 P Value 0 0010 0 581356 0 659519 0 3802 If Easter effect was estimated the following table will be displayed in the output It is clear that in the case presented below Easter has a positive significant effect on the time series on 1 level Easter easter 15 4 45711 1 30909 0 0009 The p value suggests that leap year effect is insignificant Leap year Parameter Value Std error T Stat P value leap year 0 331051 2 03402 0 8710 Demetra presents also the results of outliers detection The table includes the type of outlier its time point date parameter s value and significance Detected outliers Parameter vValue Std enor AO 4 20
53. variables are simply time series identified by their name Those names will be used in other parts of the software regression as identifier of the data Demetra considers two kinds of user defined regression variables e Static variables usually imported directly from external software by drag and drop or copy paste e Dynamic variables coming from files opened with the browsers It should be emphasized that Demetra works on the assumption that a user defined regressor is already in an appropriately centered form i e the mean of each user defined regressor is subtracted from the regressor or means for each calendar period month or quarter are subtracted from each of the user defined regressor Static variables imported directly from external software for instance Excel must be formatted as defined in the Importing data from Excel section To import them select from Workspace menu Import item and then User variables or double click item User defined variables in the Workspace tree and by drag and drop time series from Excel or use the usual keys ctrl c and ctrl v DEMETRA User Demetra User Manual final version4 doc 29 DEMETRA User Manual A Bd ia ty Bs FI 2 i G tment Variables Tools Window Help i Ge te al a By i l Ye Odpowiedz ze zmianami A o 0 RI UES SAH A XIZIRSAdc Source XCLPRVDR The figures of static variables cannot be changed Currently the only way to update static s
54. vee gt Tramo Seats eel Ei Specifi Add Existing Exclude All 7 RSA _ TramoSeatsSpec 1 7 RSA del RSAZc 2 5 Log Log window contains information about all bugs warnings and other events that took place during session Logs au J E 7281 1 DEBUG Demetra WorkspaceControl null WorkspaceControl initialized 51421 1 DEBUG TSProviders Excel ExcelVersion Strategies null ExcelVersion Strategy Excel 2007 disabled 62233 1 ERROR TS Toolkit SeasonalAdjustment Tramo Seats Monitor null Not enough observations 99061 1 ERROR TSToolkit SeasonalAdjustment Tramo Seats Monitor null EXPORTS Series LENGTH should not be gt 600 114904 1 ERROR TSToolkit SeasonalAdjustment TramoSeats Monitor null EXPORTS FOB Series LENGTH should not be gt 600 116779 1 ERROR TS Toolkit SeasonalAdjustment Tramo Seats Monitor null IMPORTS CIF Series LENGTH should not be gt 600 117998 11 ERROR TS Toolkit SeasonalAdiustment Tramo Seats Monitor null IMPORTS CIF1 Series LENGTH should not be gt 600 zi The user can also display messages which belong to a chosen category like ERROR EMERGENCY etc DEMETRA User Demetra User Manual final version4 doc 21 DEMETRA User Manual 2 6 Results panel The panel in the middle of the window is the place where Demetra displays the various object windows that it creates There could be displayed more than one window
55. window containing seasonal adjustment results TramoSeatsDoc 1 default calendar Default and user defined variables Variables DEMETRA User Demetra User Manual final version4 doc 22 DEMETRA User Manual Estimation span 7 1971 5 1983 Series has been log transformed No trading days effects No easter effect 3 outliers detected D iti trend Innovation variance 0 0104 seasonal Innovation variance 0 1890 irregular Innovation variance 0 2281 Di ti Basic checks Definition Good 0 000 Annual totals Good 0 002 20 01 1970 01 1974 01 1978 01 1982 i 01 1972 01 1976 01 1980 01 1984 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec DEMETRA User Demetra User Manual final version4 doc 23 DEMETRA User Manual 3 Application s Menu The application s menu is situated at the very top of the main window If the user moves the mouse s cursor to an entry in the main menu and click on the left mouse button a drop down menu will appear Clicking on an entry in the drop down menu selects the highlighted item The functions available in application s menu are described in the paragraphs below 3 1 Workspace menu The Workspace menu offers the following functions e New creates new Workspace displayed in the right panel e Open opens an existing project in a new window e Save save the project file named by the system under the name Workspace_ number that ca
56. 02 18 7046 3 41647 0 0000 LS 1 2007 38 5629 460194 0 0000 If the user adds a ramp regressor to the model specification range of ramp variable estimated value of coefficient and related statistics are shown in appropriate section Ramps Parameter T Stat P value rp 2010 05 30 2010 06 30 0 0104 0 0124 0 3908 If a user adds an intervention variable to the model specification estimated value of coefficient and related statistics are shown under Intervention Variables DEMETRA User Demetra User Manual final version4 doc 97 DEMETRA User Manual Pre adjustment series The table presented in this section contains series estimated by RegArima part The contents of the table depend on the effects estimated by RegArima The following items can appear here Interpolated series series interpolated for the missing observations if any o Linearized series all deterministic effect adjusted series Series corrected for the calendar effect series corrected for all calendar effects also user defined variables assigned to calendar component o Deterministic component all deterministic effects such as outliers ramps calendars etc e Calendar effect total calendar effect i e joint effect of moving holidays trading day and Easter effects Moving holidays effect the same provisionally as Easter effect o Trading day effect automatically detected or user entered trading day effects i e pre
57. 25 5 1 1993 122 0925 6 1 1993 121 9857 7 1 1993 121 9577 lt 8 1 1993 122 0333 9 1 1993 121 9712 121 8328 121 7152 121 9291 121 8648 120 7637 120 8408 120 6459 120 5538 10 1 1993 121 8328 11 1 1993 121 7152 12 1 1993 lt 1 1 1994 2 1 1994 120 7637 3 1 1994 4 1 1994 120 6459 5 1 1994 7 6 1 1994 120 3328 lt 7 1 1994 120 0606 8 1 1994 119 9265 9 1 1994 119 8885 10 1 1994 119 8396 11 1 1994 119 8378 12 1 1994 119 7315 119 5 12 1992 05 1993 10 1993 03 1994 08 1994 01 199 The history analysis plot is accompanied by information about the relative difference between initial and final estimation for the last four years For the additive decomposition absolute revisions are used for multiplicative decomposition relative differences are considered Values which absolute value are larger in absolute term than 2 times the root mean squared error of the absolute or relative revisions are marked in red and provide information about the instability of the outcome Information about mean relative difference between initial and final estimation over period displayed in table is also provided As relative difference can be positive as well as negative mean value is not very informative Magnitude of varying revisions is measured by root mean square error RMSE RMSE has the same units as the mean Relative differences mean 0 0679 msze
58. 3 2 1 2 Pre processing Main results 3 Fre adjustment series Regressors 6 Residuals z Statistics Distribution H Decomposition X11 H Diagnostics The first part of the pre processing output includes information about the data The notation of estimation span varies according to the frequencies for example 2 1993 10 2006 represents monthly and Il 1994 l 2011 represents quarterly time series number of observations actually used in the model number of parameters in the model data transformation correction for leap years and various information criteria calculated for the model Number of effective observations is the number of observations used to estimate the model i e the number of observations of regular and seasonal differenced series Number of estimated parameters is the sum of regular and seasonal parameters for both AR and MA mean effect trading working days effect outliers regressors and standard error of model DEMETRA User Demetra User Manual final version4 doc 94 DEMETRA User Manual In the pre processing part the model is estimated by exact Maximum Likelihood Estimation 2 standard error of the regression ML estimate is the standard error of the regression from Maximum Likelihood Estimation Demetra displays a maximized value of Likelihood function after iterations processed in Exact Maximum Likelihood estimation This value is used by model selection criteria AIC AICC BIC BIC Tramo defi
59. 382 10 C Tables 101 18 101899 100928 100 55 100 114 100 06 100 089 100 081 100 123 100 185 100 245 10 D Tables 2001 100 57 100 608 100 691 100 693 100 694 100 768 100 923 101 171 101 426 101 594 101 559 10 is E Tables 002 101 566 101 632 10664 101 847 102 185 102 351 102 292 102 094 101 89 101 774 101 757 10 E Diagnostics 003 101 359 101 1 100 828 100 465 100 151 99 9691 99 9146 99 907 99 8583 99 7808 99 7042 99 karian 200i 99 9209 100 02 chart ACh Ann Are Ann Aen Fa a ann Tara can Yara car Taa 64 Spectral analysis 2005 100 517 100 359 Residuals 2006 100 061 100 271 iregular 2007 101 707 101 486 SA series stationary 2008 99 8345 99 6718 Revisions history 2009 101 887 102 244 Sa Trend Sliding spans Model stability m Trading days 01 1990 01 1994 01 1998 01 2002 01 2006 01 2010 Easter mium uiy 01 1992 01 1996 01 2000 01 2004 01 2008 When a container is active its name is added to the menu toolbar DEMETRA User Demetra User Manual final version4 doc 32 DEMETRA User Manual Workspace Seasonal adjustment Chart Tools Window Help 2500000000 EXPORTS EAPORTS FOB 2000000000 1500000000 1000000000 SO0000000 01 1970 01 1975 01 1980 01 1985 01 1990 01 1995 071 2000 01 2005 01 2010 hari a i J Pytam a The chart or growth chart is automatically rescaled after adding new series Also new item Chart or Growth Chart respectively is added to menu tool
60. 6 Td B12 6 3 ri 61 1 BO TaT reo 19 2 a4 76 03821 74_Te0ST 30 49569 72 40521 BS 63957 75 44408 77 38421 8105768 Tf 97045 if Sap 8009811 81 94752 az J3711 60 5455u 78 79467 BO 2877 80 rz 79 64482 80 020 F 42243 PS 20 785 75 1566 TS 17639 T5 32247 75 6599 TE 13606 76 T3856 TT Siia TE 47556 79 36598 60 1331 BO 66752 60 8386 j 65564 BO 61593 60 2406 T3 i254 TS 6698 F 1 0 0 959287 0 35035 1 020526 0 995785 0 987861 RS Fac 0 989666 D Mrdis 0 974778 1 081156 1 051162 0 990878 0 258256 0 962189 1029257 0 996665 098709 0 391335 0 9096 17 oe aa 1 010763 034735 1 0707S8 0 127 1 137902 0 990917 1006414 10457 0 994197 0 97541 0 999501 1 015068 101r7rs 0 996765 0 577408 1000738 1 010763 0 538355 1 005841 mo Firem see DEMETRA User Manual a O A xio WCLPAVD r 73 760982 po 7a m7 po Ka B147 Sa Me EIEII 749 75441 ce E 77 EID0 768 H7 T 200 7 IH LeS Bi TTESI gira ma Tey E AGE Fam s 823971 aw 775 BOSM55 cD Bi 7E7H7 42001 BO B1277 2001 Pa BOTAZJ 75 2579 7 135 75 1764 75 6589 76 1361 5113 Ta 7366 0 131 Biois ac Boba ENEE 59 6159 a02 73 8525 a2 0 5603 1 O63 47 0 5578 0 427 0 38 0 B47 0 577 1 08176 1016 0 3508 pasg 0 9621 126 0 5366 0 98703 te Eaten Frat Fale rat TEIE aga7 1 07076 D9177 1 1719 Ekee 1 00641 1 0575 pgi mE 0 TEISE 1 01778 29561 FE n
61. 6 6 2525 8 2876 9 3277 9 3344 2 3294 5 3094 5 2865 9 2331 1 1778 5 1718 8 2101 5 mar 2753 8 2726 8 2235 7 1845 7 2170 4 2531 7 2898 7 3259 9 3321 3265 8 3052 6 2822 2232 5 1702 2 1758 8 2076 7 apr 2689 7 2670 5 2131 7 1765 5 2122 2 2487 9 2878 3203 6 3246 1 3173 8 2957 8 2703 6 2103 1 1605 7 1719 9 1973 8 may 2599 4 2567 9 2043 8 1695 4 2073 1 2445 4 2341 1 3159 6 3092 5 2867 3 2583 1985 1 1525 6 1683 4 1907 9 jun 2684 2508 3 2039 9 1687 6 2074 2437 4 2849 2 3090 9 3134 6 3071 2 2827 4 2487 6 1895 1 1455 3 1658 7 1843 9 N N tw w t RO N N Workspace panel organizes all specifications as well as processing and variables defined by the user In the specification section some specifications are already defined The user can add new specifications by choosing Add New from the pop up menu right click on the seasonal adjustment method s name In Workspace panel the user can also define calendars and regression variables The windows in which the user can define or change the seasonal adjustment parameters calendars and regression variables will be described in Chapter 3 DEMETRA User Demetra User Manual final version4 doc 19 DEMETRA User Manual E Workspace_6 El Single processing Tramo Seats gt X12 da Multiprocessing Specifications r add N RS ew RS RS Exclude All RSA3 RSA4 specifications added by use
62. 88 Description based on MARAVALL 2011 DEMETRA User Demetra User Manual final version4 doc 186 DEMETRA User Manual x a 22 g 0 s g 0 From this equation it is clear that the squared gain of the filter determines how the variance of the series contributes to the variance of the seasonal component for the different frequencies In time domain the ratio of pseudo spectra are replaced by the ratio of autocovariance generating function ACGF 89 Y B F v B F k y B F where y B F an IE yS is ACGF of s P B B F F y B F lt L y is ACGF of x P BJ B CF CF _V V a Thus Weiner Kolmogorow filter for seasonal component s is expressed as v B F k OBNO E IPB EY O B OCE Letting f A denote a pseudo spectrum One can define 0 B 0 F p B F B and 0 B contain differencing operators that make respectively and x stationary Thus for 0 B 0 F 0 B 0 F o B F V a 89 The ACGF is well defined for the stationary time series i e ACGF of B s is Via S the pseudo ACGF is calculated as 90 MARAVALL A and CANETE D 2011 DEMETRA User Demetra User Manual final version4 doc 187 DEMETRA User Manual EEANN Leal pay EO were p BA f A so f A lt f A and Tea f A ee 2 f A 80 f A lt FA Then the expression f A p A f A is the cross spectrum in time domain it is cro
63. Analyser ral Demetra UI l Color Analyser Pa Demetra XL l Demetrat XL aE Demetra XL Functions ae Demetra XL Functions ge XL Functions Examples 1 3 Uninstall previous version of Demetra In order to remove previously installed Demetrat version the user should take the following steps e Open the Add Remove Programs function in the control panel e Uninstall Demetra if listed e Close the Add Remove Programs function e Delete the Demetra home directory e Delete the program group icons if manually created 1 4 Installing Demetra Execute the file setup and follow the instructions on the screen Always take the default options i e typical installation etc 1 5 Running Demetra Start working with Demetra run the application via the newly installed Windows option under Programs or start the Demetra exe file directly from the Demetra sub folder 1 6 Closing Demetra In order to close the application the user can select File Exit from the main menu See Chapter 2 The other way is to click on the close box in the upper right hand corner of the Demetra window If you have created any unsaved work Demetra will display a warning and provide you with the opportunity to save it DEMETRA User Demetra User Manual final version4 doc 12 DEMETRA User Manual 2 Main application s windows 2 1 Overview of the software The main Demetra window which is displayed after launching the program i
64. Demetrat User Manual E eurostat I NationalBc nk CF BELGILAN Tramoseats Furcsyste Sylwia Grudkowska National Bank of Poland October 2011 DEMETRA User Manual Acknowledgements would like to thank the all the members of the Task Force on seasonal adjustment for their useful comments and helpful suggestions on various drafts of this document Thanks are due to Agustin Maravall Banco de Espa a Dominique Ladiray INSEE Jean Palate National Bank of Belgium Anna Ciammola ISTAT Faiz Alsuhail Statistics Finland Dario Buono EUROSTAT Alpay Ko ak Turkish Statistical Institute Joerg Meier Bundesbank Michael Richter Bundesbank Kevin Moore ONS and Beata Rusek NBP for their valuable support and contributions to the preparation of this Manual DEMETRA User Demetra User Manual final version4 doc 2 DEMETRA User Manual Contents COS IS neces ch Serene ese T eisene onc aan sete ne Ses Bade E E ter oee Mecsas os nese aoresscaantese 3 WUD OCHUC TION iccas ats senpsanatenddeecacsaunctonesaedtvonniaen ser peunatan adden onda nuens suka tonedeneteustcunuiece subs tansaesescauteatenoesnatenades 7 b BASIC WM EON Ue CIO Mins cuteracvedantesaamutaen ER E A 10 PADOU DC ICU a sxcavessonsccnivordunesmenensauntd auienet S 10 1 2 Demetrat application for Microsoft Excel ccsccccssseccecesscceceuesececseececeeecesseeeseseeecesseneses 11 1 3 Uninstall previous version Of Demetra t cccccc
65. EMETRA User Demetra User Manual final version4 doc 101 DEMETRA User Manual H Main results H Fre processing Reg E Tables Quality measures E Diagnostics Tables In this section key tables from the X 11 procedure are available Some tables produced by the original X 11 algorithm are omitted As an example the view of B20 table is presented below g i 3 2 5 0 A 0 Edit Bo 5 0 0 Transpose 0 right clock on the column s header or 0 0 0 table name to open the context menu pS 0 006 0 o 0 T 0 0 0 0 0 0 0 0 0 0 0 1 029 0 0 0 0 0 0 0 5 03204 0 4 388 0 0 0 0 0 0 0 0 0 0 0 0 3 281 3 8888 0 0 0 0 0 0 0 0 2 093 0 0 0 0 0 0 0 1 389 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 6286 0 0 8388 2 964 0 0 0 0 0 0 0 0 0 0 0 0 3 93974 0 0 427 0 0 467 0 0 0 0 4788 0 0 0 0 0 0 517 0 0 7325 0 439 0 0 0 0 0 0 0 0 8208 0 0 0 0 1 144 0 2 18274 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 02471 0 0 0 0 0 0 0 0 0 0 0 0 0 0 2 01573 0 0 0 0 0 A detailed list of the tables can be found in the Annex section 8A Quality measures This section presents the seasonal and trend moving filters used to estimate the seasonal factors and the final trend cycle Demetra selects the filters automatically taking into account the global moving seasonality ratio which is computed on preliminary estimates of the irregular component and of the seasonal Final fiters Trend filter 13 term
66. Example user defined trading days ListSelector DEMETRA User Demetra User Manual final version4 doc 70 DEMETRA User Manual Example Easter effect EI Trading days Type E Details Trading days Holidays El Easter effect Option Duration 4 2 4 Regression Individual Argument spec Comments Pre specified Others others ireg iuser User defined outliers are used if prior outliers nser knowledge suggest that such effects exist at known time points2 20 Definitions from X12 ARIMA Reference Manual 2007 Additive Outlier AO additive point outlier which occurred in a given date f It is modeled by variable fort t AO Ofor t t t Level shift LS variable for a constant level shift beginning on the given date It is modeled by regression variable l fort lt t fore t2t Temporary change TC a variable for a temporary level change beginning on the given datef It is i t modeled by regression variable O fort lt t Cee t t t amp fort2ty 21 In TramoSeats method this type of outlier is sometimes called by transitory change DEMETRA User Demetra User Manual final version4 doc 71 DEMETRA User Manual TramoSeas sd Individual Argument Comments spec where is a rate of decay back to the previous level 0 lt lt 1 Seasonal outliers are not supported Pre specified out
67. Kalman Filter Cambridge University Press HARVEY A C and KOOPMAN S J 1992 Diagnostic Checking of Unobseved Components Time Series Model Journal of Business amp Economic Statistics 2007 Guide to Seasonal Adjustment ONS Methodology and Statistical Development HYLLEBERG S ed 1992 Modelling Seasonality Oxford New York Toronto Oxford University Press KAISER R and MARAVALL A 1999 Seasonal Outliers in Time Series Documento de Trabajo 9915 Banco de Espana KAISER R and MARAVALL A 2000 Notes on Time series Analysis ARIMA Models and Signal Extraction Banco de Espana Working Papers No 12 Banco de Espana LADIRAY D and QUENNEVILLE B 1999 Seasonal Adjustment with the X 11 Method Lecture Notes in Statistics 2001 New York Springer Verlag LADIRAY D and MAZZI G L 2003 Seasonal Adjustment of European Aggregates Direct versus Indirect Approach Proceedings of the Seminar on Seasonal Adjustment MANNA M and PERONACI R ed European Central Bank 37 66 LOTHIAN J and MORRY M 1978 A Test for Presence of Identifiable Seasonality when Using the X 11 Program Working Paper Time Series Research Division Statistics Canada Ottawa ON Canada LJUNG G and BOX G 1979 The likelihood function of stationary autoregressive moving average models Biometrika 66 265 270 MARAVALL A 1987 Minimum Mean Squared Err
68. LEY D MONSELL B C SHULMAN H B and PUGH M G 1990 Slidings Soans Diagnostics for Seasonal and Related Adjustments Journal of the American Statistical Association vol 85 n 410 GOMEZ V and MARAVALL A 1994 Estimation Prediction and Interpolation for Nonstationary Series with the Kalman Filter Journal of the American Statistical Association vol 89 n 426 611 624 GOMEZ V AND MARAVALL A 1994 Estimation Prediction and Interpolation for Nonstationary Series With the Kalman Filter Journal of the American Statistical Association vol 89 n 426 611 624 GOMEZ V MARAVALL A 1997 Programs TRAMO and SEATS Instructions for the User http www istat it strumenti metodi destag software manualdos pdf DEMETRA User Demetra User Manual final version4 doc 207 DEMETRA User Manual GOMEZ V MARAVALL A 1998 Seasonal Adjustment and Signal Extraction in Economic Time Series Banco de Espana Working Papers 9809 Banco de Espa a GOMEZ V and MARAVALL A 2001 Seasonal Adjustment and Signal Extraction in Economic Time Series in A Course in Advanced Time Series Analysis PENA D TIAO G and TSAY R eds Wiley and Sons New York 202 246 HANNAN E J and RISSANEN J 1982 Recursive Estimation of Mixed Autoregressive Moving Average Order Biometrika 69 81 94 HARVEY A 1989 Forecasting Structural Time Series Models and the
69. OMEZ V MARAVALL A 1997 DEMETRA User Demetra User Manual final version4 doc 182 DEMETRA User Manual 5A TramoSeats method TramoSeats is a model based seasonal adjustment method developed by Victor Gomez and Agustin Maravall Bank of Spain It consists of two linked programs Tramo and Seats Tramo Time Series Regression with Arima Noise Missing Observations and Outliers performs estimation forecasting and interpolation of regression models with missing observations and Arima errors in the presence of possibly several types of outliers Seats Signal Extraction in Arima Time Series performs an Arima based decomposition of an observed time series into unobserved components Information about TramoSeats method the user find below derives directly from papers by GOMEZ V and MARAVALL A Pre processing in Tramo Program Tramo fits the following regression model to the original time series z y x where B f 8 vector of regression coefficients Y Yp Yar 7 N regression variables trading days variables leap year effect outliers Easter effect ramps intervention variables user defined variables x term that follows the general Arima process B O B v O B a where B is the backshift operator 0 B 9 B and 6 B are finite polynomials in B a is a white noise variable with constant variance Parameters of the ARIMA model are estimated using Hannan Rissanen algorithm Hannan Ri
70. Those windows will overlap each other with the foremost window being in focus or active The active window has a darkened title bar X12Doc 11 Tools Window Help E Koniunktura w przemy le E Single processing TramoSeats B X12 X12Doc 1 X12Doc 6 X12Doc 9 El sa Multiprocessing _ SAProcessing 2 SAProcessing 1 SAProcessing 3 SAProcessing 4 E as Specifications TramoSeats RSAO RSA1 RSA2 RSA3 RSA4 RSA5 I X12 X11 j RSAI RSA2c RSA3 _ RSA4c RSA5c X12Spec 1 X12Spec 2 f2 Calendars KE TramoSeatsDoc 5 A Fotimatinn onan 141 1000 44 2n41M aans RE X12Doc 11 Diagr X12 RSA5c Source XCLPRVDR Name CPICAPITALCITY Pre processing R ima Estimation span 2 1980 1 2009 No trading days effects x xi _ Name Unemployment D 1 BD 1 Estimate oS ry A 8 o Ei Jan Feb Mar Apr May Jun Jul Aug Sep The windows in the results panel can be arranged in many different ways depending on the user s needs see 3 5 The example below shows one of the possible displays of this panel The right part of the panel presents navigation tree while on the left the actual results are displayed The user can execute several seasonal adjustments and define some regression variables The results are displayed in consecutive bookmarks which allow the user to switch them over On the picture below it is shown that tree panels are opened
71. User Manual final version4 doc 124 DEMETRA User Manual e Easter effect parameter stability 0 0 005 0 01 0 015 0 02 0 025 0 03 Easter e Arima parameters stability Theta 1 BTheta 1 DEMETRA User Demetra User Manual final version4 doc 125 DEMETRA User Manual Small deviations from the mean parameter value are preferable Taking into account a scale on the vertical axis the most significant differencies between paramteres values took place for Arima model parameters 4 3 2 2 TramoSeats The basic output structure is as follows e Main results o Charts o Table o S I ratio e Pre processing Tramo o Pre adjustment series o Arima o Regressors o Residulas e Decomposition Seats o Stochastic series o Model based tests o WK analysis e Diagnostics o Seasonality tests o Spectral analysis o Revisions history o Sliding spans o Model stability TramoSeats method and related concepts are presented in the Annex section 4A Detailed description of the seasonal adjustment outcomes is presented below For those features that are very similar to the X12 appropriate descriptions and drawings are omitted The user can find DEMETRA User Demetra User Manual final version4 doc 126 DEMETRA User Manual those in Seasonal adjustment results for X12 In this section only issues specific for TramoSeats will be discussed in detail 4 3 2 2 1 Main results Basic information ab
72. ach component follows the general Arima model 0 B x Y Ba Where i trend seasonal transitory or irregular components 3 respectively a denotes a white noise variable 0 B p B the polynomial yw B The polynomials 6 B B and 6 B are of finite order A white noise variable is normally identically and indecently distributed and has a zero mean and variance of the one period ahead 83 For irregular component it is an ARIMA 0 0 0 0 0 0 model DEMETRA User Demetra User Manual final version4 doc 184 DEMETRA User Manual forecast error for the observed time series V a x also follows Arima model of the type O B x w B a where a is a white noise variable with variance V a In an unobserved components model residuals a are estimators of the disturbances associated with the unobserved components These residuals are functions of the innovations one step ahead prediction errors and are called pseudo innovations Demetra uses term innovations which should be understand as pseudo innovations 4 W B y EF The pseudo spectrum of x is the Fourier transform of and is denoted by g Q where is a frequency argument and F is a forward operator for which F B For particular realization of X cae ee x Seats aims to obtain for each component the estimator Xinr such that e z x 1X fi minimized it is Minimum Mean Square Error MMSE estimator Under the j
73. anual final version4 doc 8 DEMETRA User Manual Selected aspects of seasonal adjustment methods and technical issues are described in the Annex Instead of X 12 Arima Demetra uses notation X12 For this reason this notation is used further in this Manual DEMETRA User Demetra User Manual final version4 doc 9 DEMETRA User Manual 1 Basic information 1 1 About Demetrat The first release of Demetra contains Demetra itself main graphical interface and Excel add ins ColorAnalyser Demetra XL and XL Functions More information about Excel add ins is available in 1 2 Demetra Application for Microsoft Excel Demetra version 1 0 uses the following core engines e TramoSeats dlls dated 8 2009 e X12 dll used in Demetra 2 2 The most important results including the complete RegArima model directly come from the core engines All the diagnostics are computed outside the core engines see below One of the strategic choices of Demetra is to provide common presentation analysis tools for both TramoSeats and X12 Thus of that the results from both methods can be easily compared This implies that many diagnostics statistics auxiliary results etc are computed outside the core engines Demetra is of course highly influenced by the output of TramoSeats and of X12 Most analyses presented in Demetra are available in the core engines However the results with TramoSeats and X12 may slightly differ for a lot of reasons
74. appropriate box in left hand side of the Output window The settings which are displayed in the other part of the window come from Tool gt Options menu All changes in those settings should be done in the Tool gt DEMETRA User Demetra User Manual final version4 doc 172 DEMETRA User Manual Options menu If the user changes the settings e g output s folder in the SAProcessingXXX gt Generate output window or TSProcessingXXX gt Generate output it will not have any effect on the output s content SAProcessing 2 Update reports Edit Priority mark the output s type Add to workspace Initial order these settings must be specified in the tool gt options menu am For multi processing which doesn t belong to a workspace output files name is default demetra If multi processing is saved in the workspace the multi processing s name is used 4 4 6 Assigning priority to the series Priorities are simple indicators from O to 10 that users can use to mark series that require more or less attention The software is able to compute automatically priorities based on the average of the logged series By default priority is not calculated DEMETRA User Demetra User Manual final version4 doc 173 DEMETRA User Manual Be SAProcessing 6 Series Method Estimation Processing Priority Quality Warning Industries alimentaires 001 X12 R5 Concument Valid Transformati
75. articular case O0 lt lt 1 11 11 See BOX G E P and TIAO G C 1975 DEMETRA User Demetra User Manual final version4 doc 56 DEMETRA User Manual Comments Individual Argument spec User defined regression user The user defined variables effect can be variables usertype assigned to the trend irregular holiday or can exist as an additional component option Undefined For practical considerations seasonal effects are currently not supported The user can specify the structure of the lags 2 When regression variable Var is introduced a with first lag l and last lag Demetrat estimates the following regression model for this variable Var B x t l 6 x t l To estimate Var p x t L The user should put first lag last lag 1 If first lag O and last lag 12 it means that in addition to instantaneous effect the effect of variable Var is soread over one year Example Pre specified outliers Transformation Uo J ae 1 2000 Calendar effects 1 Is 8 2008 E Arima modelling Intervention variables Outliers detection User defined variables _ Estimation 12 The user can find more details and examples in MARAVALL A 2008 DEMETRA User Demetra User Manual final version4 doc 57 DEMETRA User Manual Example Ramps X12 specications Ea Regression o 7 evention variables RampProperties Example Intervention variables
76. asonal factors are presented in the S ratio chart 4 3 2 2 2 Pre processing Tramo DEMETRA User Demetra User Manual final version4 doc 130 DEMETRA User Manual E Main results Pre processing Tramo E Residuals E Decomposition Seats oe Diagnostics Pre processing section is organized in the similar way in TramoSeats and X12 For details refer to RegArima description 4 3 2 1 2 Major differences between methods concern mostly Arima section Pre adjustment series The table presented in this section includes e series corrected by Tramo i e o interpolated series o linearized series o series corrected for calendar effects if calendar effects are not specified it is the same as the interpolated series e deterministic effects detected and estimated by Tramo i e o deterministic component o calendar effects o trading days effect o moving holidays effect o outliers effect on trend component o outliers effect on irregular component o total outliers effect o regression effect on seasonally adjusted series 53 For particular time series the pre processing table results includes only those deterministic effects that has been detected during estimation DEMETRA User Demetra User Manual final version4 doc 131 DEMETRA User Manual o regression effect on the trend component o regression effect on the irregular component o regression effect on the seasonal component Arima Arima se
77. aster effect in use B Arima modelling ls enabled True ular AR 1 0 77611 B 0 39114 B 2 0 17295 Bz Automatic modellinc Pretest Add isonal AR 1 Arima ular MA 1 iu Muitliars datactian If the option has been used inappropriately used calendar effect is present but the user decided not to estimate them the result will be clearly seenin spectral function computed in pre processing part 4 5 2 Saving and refreshing workspaces By default single and multi processing generated through the so called short ways are not put in the current workspace To be able to save and to refresh them the user must first add them to the workspace That can be done for instance through the main menu SAProcessingXXX gt Add to Workspace SESS Specification Co py d Paste Lock The user still has to save the workspace using the usual menu command Save DEMETRA User Demetra User Manual final version4 doc 177 DEMETRA User Manual Workspace eS Open Hm Save AS View Edit Import Recent Workspaces Exit When Demetrat is re opened it will automatically open at the last used workspace The software also maintains a list of the most recently used workspace which can be easily accessed Workspace be Hew E open bd Save aif Save AS View Ede d m pecent Workspaces F LANPRD DFS MNGIUSERS HOMETPALATE N Demetra workspace _2 xml Ex A saved item of a workspace can be op
78. ates the processing after changes in seasonal adjustment specifications Refresh refreshing a processing with new data Edit allows adding new times series to the list using multi processing wizard and pasting previously cut time series again in the list Last three edit options Cut Copy and Delete are active if the time series was marked on the list see description below Priority indicator that users can use to mark series that require more or less attention Priorities take values from O to 10 Demetra computes them automatically based on the average of the logged series The user can chose the method of computation log based or level based Save saves the processing Generate output offers a set of output formats txt XLS ODBC CSV CSV matrix the choice of the folder that will contain the results in the example below the file will be saved on disk C Documents and Settings and the content of the exported file Add to workspace adds the multi processing to the workspace s tree Initial order displays times series on the list in initial order The option is useful if the list has been sorted by other column e g by quality or method DEMETRA User Demetra User Manual final version4 doc 163 DEMETRA User Manual After defining a multi processing the user should execute the estimation using Run option After that it is possible to Generate output The Save option is inactive as soon as t
79. ation procedure vap Unit root limit for final model 25 See the Annex section 5A DEMETRA User Demetra User Manual final version4 doc 77 DEMETRA User Manual TramoSeatsSpec 3 f x EML estimation True Frecision 0 0001 0 94 Ubp bp Unit root limit for final model Cancel OK 4 2 9 Decomposition Seats ae Comments Individual spec F model Seats noadmiss When model does not accept an admissible parameters decomposition force to use an approximation xl orce MA unit root Seats When the modules of n estimated root falls boundary parameters in the range x 1 it is set to 1 if it is in AR it is set equal to x if root is in MA Trend boundary Seats mod Trend boundary is defined for the modulus parameters of the AR root If real positive root is equal or greater than that value the AR root is integrated in the trend component Below that value the root is integrated in the transitory component Seasonal Seats Tolerance measured in degrees to allocate tolerance parameters AR roots into the seasonal or the transitory component x Calendar effects H Arima modelling Seasonal tolerance ed Outliers detection DEMETRA User Demetra User Manual final version4 doc 78 DEMETRA User Manual 4 3 Single processing Demetra offers several ways to define seasonal adjustment of a single time series A key question which will determine the best way to proceed concerns the specifi
80. bar Putting numerous time series into one chart could make it confusing In this case the user can click on one series which is then displayed in bold 3000000000 EXPORTS EXPORTS FOB IMPORTS CIF 2500000000 IMPORTS CIF Jj I y 2000000000 Fi i 1 ily iv 1500000000 HH pil 1E P l 1000000000 AEA Ae Li ANN TATEA AA Erra 500000000 VI 01 1970 01 1974 01 1978 01 1982 01 1966 01 1990 01 1994 01 1998 01 2002 01 2006 01 2010 01 1972 01 1976 01 1960 01 1964 01 1966 01 1992 01 1996 01 2000 01 2004 01 2008 The right button menu offers many useful options Its content depends on the type of container For example for the growth chart the following options are available Copy copies raw series and allows to paste it e g into Excel The function is active if the user clicks on the time series in the chart Copy growth data copies m m or q q growth rates of the marked time series and allows to paste it e g into Excel The function is active if the user clicks on the time series in the chart Remove removes time series from the chart The function is active if the user clicks on the time series in the chart Copy all copies all raw time series and allows pasting it into e g Excel DEMETRA User Demetra User Manual final version4 doc 33 DEMETRA User Manual Copy all growth data copies m m or q q growth rates of the time series and allows to paste it e g into Excel Remove all
81. cation that will be used to start the analysis 4 3 1 Defining a single processing The first step to produce a fast seasonal adjustment is to create a processing The user can take the existing specification or create completely new specification First category includes pre defined specifications and specifications previously defined and saved by the user The second solution is to create the new specification for the needs of seasonal adjustment of particular time series This can be done when a user wants to use in a frequent way a specification that is not available in the list of the predefined ones for example if one wants to integrate systematically its own calendar variables or if one want to exclude some kinds of outliers After creating a new specification it can be added to the user s workspace 4 3 1 1 Creation of a single processing using existing specification Single processing can be launched in two different ways 1 by activating the specification or drag drop the specification The user could activate the specification from the list displayed in the workspace panel before choosing the series By default RSA5c is ticked The procedure is as follows e Select in the Workspace tree the specification you want to activate e Open the local menu by means of the right button of the mouse e Choose the Active option from pop up menu DEMETRA User Demetra User Manual final version4 doc 79 DEMETRA User Manual Work
82. ci E RA 160 4 4 2 2 Mu lti proc ssing MENU sivasccessisvccsssceset dik ves cd desecadsvcncadiecvcuscevacebelssitertetouveessdes 163 4 4 2 3 Detailed results and modification of the Specification cccceeseeceeeeeeeeeeeees 164 44 3 PErIOO tO DeriOd Gata ProductioN jsccsaierziesdeiencccacetentecidavandednstenelabeesd a 168 4 4 4 Further explanations on the refreshing Of multi processing ccccccesececeeeeseeeeeeeees 171 4 4 5 Sending the results to external devices cccccccssseccceeseececceescceceeececeueeceecenecessuneces 172 4 4 6 Assigning Priority tO THE SETICS cccccceeseccccesecccceeseeccceesececceesccessueceecueceeeeesecetsuneses 173 4 5 Additional TUM CTIONS i r iGssscatasosa can A E 176 4 5 1 CHANGING the SPCCINICALION seco tens chet ticosstencs a daadeceapietecys a a 176 4 5 2 Saving and retreshinge WOrkKSPACeS cic vacate teicarh ati eats TTAN 177 ANNEX carora ei a E E nedbisiancoastagrh end cerceani Denes Sie toon Gncsseeiden E A TEDE 180 IA Defmitonmoftheresiduals cisicssabsdaasndedessoanbiaaaavaiurcavnee ENON 180 2A Least squares estimation by means of the QR decomposition sssessssssrrersssrrresrrrrerrrressne 180 A 01 21 TON arana Seton eon ey ena RROnEY SEI eC ren Er me eee Sree eee 181 OAR WOGEISCIECTION Criteri anmi a E R 182 DEMETRA User Demetra User Manual final version4 doc 5 DEMETRA User Manual DA MANAG SEAUS IMSL NOG seisa e r Gods scan thdakion th exusa ues
83. complete seasonal adjustment model automatically so the results are updated immediately DEMETRA User Demetra User Manual final version4 doc 44 DEMETRA User Manual Copy Paste Lock x1 2Do0c 5 Add to workspace I afrecf Beane RegAnme H Decomposition X11 F Diagnostics O Trading days Type ElI Easter effect ls enabled Detailed description of the X12 specifications is presented in Chapter 4 1 The option Specification from results works in the similar way as the Current specification It is active when the processing has been executed Add to workspace adds the single processing to the workspace s tree Copy copies item chosen by the user Results Processing Current specification Specification from results Paste pastes the item previously copied 3 4 TramoSeats Doc This item is added to the application s menu when seasonal adjustment using TramoSeats method has been previously executed and after that it has been activated by the user This item offers the similar options set as the X12Doc Detailed description of the TramoSeats specifications is presented in Chapter 4 2 TramoSeatsDoc 1 Specification Current specification Copy gt Paste Lock Add to workspace DEMETRA User Demetra User Manual final version4 doc 45 DEMETRA User Manual 3 5 Window menu Window menu offers the following functions e Floating show additional infor
84. ction shows the theoretical pseudo spectrum of the Arima model estimated on the series graph on the right and the theoretical autocorrelation function of the stationary arma part of the model graph on the left The theoretical pseudo spectrum is displayed in the top left part The blue line represents Arima model identified by Tramo If this model has been changed by Seats a second line in magenta corresponding to the new Arima model is overlapped The theoretical auto correlation of the stationary arma part of the model estimated in Tramo is presented in the top right part in blue If such model is changed by Seats a second theoretical correlogram is shown in magenta In the bottom part estimated coefficients of parameters regular and seasonal AR and MA are shown in closed form i e using the backshift operator B 1 1 08 05 l 0 6 i OQOOOOOOOO0O OOOOOOOOO0O00000000000000 0 4 Oo 0 5 02 0 Pli2 Pl 5 10 15 20 25 30 35 Tramo model Polynomials regular AR 1 seasonal AR 1 0 81888 5 regular MA 1 seasonal MA 1 0 271955 Seats model Polynomials regular AR 1 Seasonal AR 1 regular MA 1 seasonal MA 1 0 42819 5 In this part frequencies corresponding to regular AR roots are also reported if present This frequencies may represent tading day effect or cycle of transitory component to be extracted in Seats DEMETRA User Demetra User Manual final version4 doc 132 DEMETRA User Manual 0 6 5 0 6 Og
85. cy 25 which means that 25 the sliding spans statistics are in this interval Distribution 25 00 20 00 15 00 10 00 5 00 0 00 in 0 001 0 02 0 03 0 04 0 05 0 06 0 07 0 08 0 09 44 In frequency polygon data presented on the horizontal axis are grouped into class intervals DEMETRA User Demetra User Manual final version4 doc 121 DEMETRA User Manual According to the FINDLEY D MONSELL B C SHULMAN H B and PUGH M G 1990 the results of seasonal adjustment are stable if the percentage of unstable abnormal seasonal factors less then 15 of total number of observations Empirical surveys support the view that adjustments with more than 25 of the months or quarters flagged for unstable seasonal factor estimates are not acceptable Therefore the user should check the total frequency of the intervals between 0 03 and 1 The last panel contains detailed information about the percentage of values for which the sliding spans condition is not fulfilled In the example presented below 4 3 of values has been marked by the sliding spans diagnostic as abnormal Moreover Demetra provides information about number of breakdowns of unstable factors and average maximum percent differences grouped by month or quarter and by year It gives idea weather observations with unreliable adjustment cluster in certain calendar periods and whether their sliding spans statistics barely or substantially exceed the threshold The
86. d by the Committee on Monetary Financial and Balance of Payments statistics CMFB and the Statistical Programme Committee SPC as a framework for seasonal adjustment of Principal European Economic Indicators PEEIs and other ESS and ESCB economic indicators ESS guidelines focus on two most commonly used seasonal adjustment methods i e TramoSeats and X 12 Arima and present useful practical recommendations Both methods are divided into two main parts First one is called a pre adjustment and removes the deterministic effects from the series by means of a regression model with Arima noises Second one is the decomposition TramoSeats and X 12 Arima use a very similar approach in the first part of the processing but they differ completely in the second part of the algorithm Therefore the comparison of the results is often difficult even for the modelling step Moreover their diagnostics focus on different aspects and their outputs take completely different forms Eurostat faced a huge challenge of improving comparability of the results and diagnostics from both methods in existing Demetra because this software was not flexible enough Moreover 1 TramoSeats is a model based seasonal adjustment method developed by Victor Gomez and Agustin Maravall Bank of Spain It consists of two linked programs Tramo and Seats Tramo Time Series Regression with Arima Noise Missing Observations and Outliers performs estimation forecasting and interpolat
87. dded to the list of seasonally adjusted items in the multi series processing Add items part is not about adding time series to the regression part of the pre adjustment model but simply shows the user the list of time series which have been chosen in the first step It is not possible to add new time series to the multi processing here DEMETRA User Demetra User Manual final version4 doc 159 DEMETRA User Manual Multi processing definition wizard Choose series Add items Finishing The defined items series specification will be added tot the list of SAA items in the multi seres processing At the last stage of the wizard Finishing the user can modify the name of the multiprocessing SAProcessing xx default one can also add the multi processing to the workspace for future re use and the user can decide if the execution is automatically started the default when the wizard is closed It should be mentioned that the user can go back to the first step of the wizard at any time if one wants to add other series with other specifications 4 4 2 Seasonal adjustment results for multi processing 4 4 2 1 Generalities The outcome of the multi processing is presented in the window which contains three panels The first panel Processing gives an overview of the processing of each series and more especially of the diagnostics computed by Demetra on its seasonal adjustment Some warnings can also
88. different statistical algorithmic choices possible bugs In any case the global messages of seasonal adjustment are nearly always similar Amongst the most important tools implemented in Demetra the following functionalities should be mentioned e Likelihood X12 like RegArima model t stat as in Tramo RegArima model was re computed in Demetrat X12 Tramo and Stamp like solutions available in the framework e Residuals analysis Tramo like but based on another set of diagnostics e Seasonality tests X12 like e Spectral analysis X12 definition e Sliding spans X12 e Revision history e Wiener Kolmogorov analysis Seats like Solutions implemented in Demetra lead to more flexible software New features are easy to add to the software without modifying the core engine One of the key features of Demetra is the possibility to use the underlying algorithms through a rich application programming interface API This feature allows the integration of the routines in very different contexts as well as the building of new applications The most important concepts time series seasonal adjustment developed to encapsulate the core engines are common to both algorithms The code for making DEMETRA User Demetra User Manual final version4 doc 10 DEMETRA User Manual basic seasonal adjustment is straightforward However it is possible to use the API to solve very tricky problems A minimalist example is provided
89. dominated by highly moving seasonality The testing procedure is shown below 102 DAGUM E B 1987 DEMETRA User Demetra User Manual final version4 doc 204 DEMETRA User Manual Test for the presence of stable seasonality at 0 1 level F H not rejected H rejected Test for the presence of moving seasonality at the 5 level Ly H not rejected H rejected Test for the presence of identifiable Test for the presence of identifiable seasonality seasonality 7 aly i 7 3F 0 5 e a F F F F T a T B Failure if T 21 7 3 F Failure if 1 or a gt S F H not rejected H not rejected H rejected Non parametric Kruskal Wallis test at the 0 1 level H not rejected H rejected No identifiable seasonality Probably no identifiable Identifiable seasonality present seasonality present present 13A Code to generate simple seasonal adjustments C Some namespaces have been removed to simplify the reading creates a new time series parameters frequency first year first period 0 based array of doubles copy data uses the current array or creates a copy TSData s new TSData 12 1967 U g_prodind false basic processing tramo seats specification RSA5 full automatic TramoSeats Specification ts_spec TramoSeats Specification RSA5 launches tramo seats core engine DEMETRA User Demetra User Manual final version4 doc
90. e For each autoregressive and moving average parameters the user can specify its initial value used in this estimation a Comments Individual spec Mean regression variables It is considered that the mean is part of the Arima model it highly depends on the chosen model P D Q BP BD arima model Parameters of Box Jenkins Arima model BQ P D QO BP BP BQ P nonseasonal autoregressive order D nonseasonal differencing of order D Q nonseasonal moving average order BP seasonal autoregressive order BD seasonal differencing of order BD BQ seasonal moving average order theta btheta arima theta initial values 1 for nonseasonal phi bphi seasonal autoregressive parameters phi initial values for nonseasonal autoregressive parameters btheta initial values for seasonal autoregressive parameters bphi initial values for seasonal moving average parameters The user can choose the Arima model manually In the example below Arima model 1 2 1 0 1 1 has been specified 15 Initial values are described in the Annex Chapter 6A DEMETRA User Demetra User Manual final version4 doc 60 DEMETRA User Manual X1275pec 1 Basic Mean False Z The value of each parameter can be estimated automatically by the program using initial value if specified or fixed by the user at initial value In order to introduce fixed parameter s value the user should click on the parameter name
91. e model RSA3 Log level outliers detection automatic model identification model identification Log level trading days Easter outliers detection automatic model identification Log level working days Easter outliers detection Airline RSA2c model pre adjustment for leap year if logarithmic transformation has been used Log level working days Easter outliers detection automatic RSA4c model identification pre adjustment for leap year if logarithmic transformation has been used Log level trading days Easter outliers detection automatic RSA5 model identification pre adjustment for leap year if logarithmic transformation has been used Explanations for settings No pre processing RSA1 Log level outliers detection Airline model X12 Level no transformation is performed Log level Demetra tests for the log level specification Working days a pretest is made for the presence of the working day effect by using one parameter specification working vs non working days Trading days a pretest is made for the presence of the trading day effect by using six parameters specification for working days the day of week Monday Fridays specified Easter the program tests for the necessity of a correction for Easter effect in the original series DEMETRA User Demetra User Manual final version4 doc 181 DEMETRA User Manual Outliers detection Demetra automatically detects all types of ou
92. e the refreshing options could be to a large extent useless The user can change the specification of a series at any time What they change manually is actually the reference specification which is used for the current processing but also for future re estimations Considering the design of Demetra the convenient way for processing many series in a recurrent production context might be as follows 1 Chosen a large specification that will be applied on the set of series 2 Modify the specifications that produce bad results Try to minimize the restrictions you impose on the specification 3 Save the processing which is the basis for all the next steps 4 During one year refresh for each new period the processing without changing too much the model typically use the Parameters option Modify with caution any unacceptable results that could be generated by the new data new outliers 5 After one year carry out a more serious revision for instance All outliers 4 4 5 Sending the results to external devices When the multi processing is created it is possible to generate several outputs Excel workbook csv files through the main menu command SAProcessingXXX gt Generate output or TSProcessingXXX gt Generate output It should be noted that Excel and csv outputs will be put in the temporary folder if their target folders are not specified The user is expected to choose the output format by marking the
93. e k 1 and n k are degrees of freedom The number of observations in preliminary estimation of the unmodified Seasonal Irregular is lower than in final estimation of the unmodified Seasonal Irregular component Because of that the number of degrees of freedom in stable seasonality test is lower than number of degrees of freedom in test for the presence of seasonality assuming stability see 4 4 3 e g X12 uses centered moving average of order 12 to calculate the preliminary estimation of trend cycle As a result the first six and last six points in the series are not computed at this stage of calculation Preliminary estimation of trend cycle is then used for calculation the preliminary estimation of the unmodified Seasonal Irregular If the null hypothesis of no stable seasonality is not rejected at the 0 10 significance level P 20 001 then the series is considered to be non seasonal e Kruskal Wallis test Kruscal Wallis test is a non parametric test used for comparing samples from two or more groups The null hypothesis states that all months or quarters respectively have the same mean The test is calculated for the final estimation of the unmodified Seasonal Irregular component from which k samples A are derived k 12 for monthly series and k 4 for quarterly series of size n N n respectively The test is based on the statistic ko Ne ze gt 3 n D g n n l a n where S is the sum of the ranks of the ob
94. e ratio of component innovation variance to series innovation variance The variance of the irregular component is maximized while the others are minimized considering the rule of canonical decomposition Therefore it is expected that k irregular would be greater than remaining k An example of the output is presented below trend Innovation variance 0 0972 seasonal Innovation variance 0 0551 irregular Innovation variance 0 1684 If some components have not been extracted by Seats from related time series e g transitory component they are not displayed in this section 50 In order to identify the components Seats assumes that components are orthogonal to each other and each component except for the irregular one is clean of noise This is called the canonical property and implies that no additive white noise can be extracted from a component that is not the irregular one 51 GOMEZ V and MARAVALL A 1998 52 GOMEZ V and MARAVALL A 1998 DEMETRA User Demetra User Manual final version4 doc 129 DEMETRA User Manual The Diagnostics includes the most important statistics which are informing the user about quality of the seasonal adjustment by reporting a summary of diagnostics Summary Basic Checks Visual spectral analysis regarima residuals residual seasonality and outliers parts have been already described in 4 3 2 1 Seats diagnostics is characteristic only for TramoSeats method and shows res
95. eats Dec ition Seats Estimation span 1 1990 8 2009 X X12 E Transformation et conservation de la viande et pr par TramoSeats Transformation et conservation de fruits et legumes 00 Decomposition Seats RSA1 Fabrication dhuiles et graisses v g tales et animales RSA2 Fabrication de produits laitiers 001563340 trend Innovation variance 0 0097 RSA3 3 4 seasonal Innovation variance 0 0554 Travail des grains fabrication de produits amylac s irregular Innovation variance 0 5019 RSA4 Fabrication de produits de boulangerie patisserie et de Fabrication d autres produits alimentaires001563349 Fabrication d aliments pour animaux 001563352 Fabrication de boissons 001563041 Fabrication de produits base de tabac 001564044 FRANCE Mat lect 21 FRANCE Mat transport FRANCE Textile 9 EE ia yeh Mig se results of seasonal adjustment are tihi i 80 10 9 presented in the central panel chek aah aerad SAAR SRT gt 01 1995 01 2005 FebApr JunAug Oct Dec The results contain a set of detailed panels organized in tree displayed in the left panel of the output window The user can go through them by selecting a node in the navigation tree of the processing The current specification and the current series are displayed on the top of the window Demetra presents several charts and tables with the results of seasonal adjustment and
96. el is attached to the stand alone Demetra The applications are called Excel add ins The aim of this tool is to provide in the Microsoft Excel environment a seasonal adjustment tool inspired from the Demetra stand alone application The application is designated for efficient multiprocessing hence information about quality is limited in comparison to Demetrat Using Excel add ins the user can easily and quickly calculate the seasonal adjustment for a whole table of time series in the frame of an Excel workbook with detailed results for each series in separate worksheets Both TramoSeats and X12 methods are available The Demetra application for Microsoft Excel is delivered as a usual workbook in two versions one for the Excel 2003 Demetra xls and one for Excel 2007 Demetra xlsm The workbook contains only the application code in VBA The code structure is available for users Demetra application for Microsoft Excel consists of e ColorAnalyser a tool to search outliers in an Excel worksheet containing time series DEMETRA User Demetra User Manual final version4 doc 11 DEMETRA User Manual e Demetra XL a seasonal adjustment tool in the Microsoft Excel environment inspired by the Demetra which can be used for multiprocessing e XL Functions Set of Demetra Excel functions Manuals for applications are attached to the software The picture below shows how to find them fg Demetra 1 02 riley Ex aT Color
97. ened by a double click or by its local menu It is then showed in its previous state Demetra proposes several options to refresh it7 Update reports Refresh Current adjustment partial Edit b Partial concurrent adjustment Parameters Priority b Concurrent adjustment Last outliers params All outliers params Generate output a p Arima and outliers params Save l ta uoarkoomare AJJ Initial order 79 For the moment those options are only available for multi processing DEMETRA User Demetra User Manual final version4 doc 178 DEMETRA User Manual Parameters Only the model parameters are refreshed The order of the Arima p d q P D Q is unchanged Outliers params Outliers and model parameters are re estimated Last outliers params Outliers on the last year and model parameters are re estimated Complete The model is completely re estimated When the refresh option has been selected Demetra automatically goes to the suitable time series provider s to ask for the updated observations the new estimations are done on these series using the previous models modified by the chosen option The example below presents results obtained by applying option Last outliers params Outliers are divided into two sections pre definied outliers outliers detected during penultimate execution of the multi processing and detected outliers outliers identified in spa
98. enncumees 34 sL P a S 35 BoP DHCTEnN NE o E act ees 36 Ze OPUNE oe E E sonst 37 DEMETRA User Demetra User Manual final version4 doc 3 DEMETRA User Manual i UZ DOC essa aaiahina cients tac E S bacon eo seach a nance sagen ul ceeeaci S 44 34 ThalmOse ats DOC cists incised ciate aes cea A N 45 30 WV INOW MEN Uceira ewes aiaarn vs oylnaa ea oa wom usiecies ualeaiaw vn aye cauca eaem sins eseman ec eeea ee 46 4 SOAS OM alli CUSED sacisarecses cassettes asset saree ttsteta a a geass N 48 Oe Dede PECCI OR ee sete eea aa eion detec outseintto seat rat ca te aa ae Seka pan ama icesteoecncancuaanenueueren eee akan 49 AAAs GONEFAVCCSErIDUION sisstcsueishcgavaoeeteatedeascsutays son vanesaasunansauanesssonsanuiecaemaotedcoutaabtanss een aeeaeaes 49 MDD BASIC cnt iir aE swenach T sired E E N A ee ceaetedds 50 Medi Mansa ON ee n a NE T O ecouata Goureeetatand extenders 50 ATA Calendir eects ronie E N A N 51 A 5s REPES SION encre E E Rall a 55 ALG Automatic Modeling srie a aN 59 BD is ANM an E E inte ENE E ek euestesbasatdtnanntans 60 Are Ouers detedtiOnNeenes e a a tenes 62 Abe ESMAO aeea A hal ahaa hee E alse rena at 64 A AO IDE COMMIOSITIOIN IN e A iiacauazaudvaen du cameasatinsevasaatwausaeeses 64 42s kamo ets SDECITICALIONS asna estos E a N 66 A de General GSS CHIDUION ga a a a a a 67 4 22 rastom NoNe T A A ENa TAN 67 ADS CAlMGak eneco eani N 68 AZA RCELES SION espen a E E soneunieensiaetien 71 4 2 5 Arima modelling aut
99. ent estimators This graph gives information about the time needed by the concurrent estimators to converge to the final ones As stressed in Maravall 1995 large revisions are associated to highly stochastic components and converge fast while smaller revisions are implied by very stable components and converge slowly On the graph below X axis presents periods 0 means the last available observation and the Y axis shows the decrease in size of the standard error of the revision in percentages For the particular time series presented on the graph below after one year of additional data 12 observations the percentage reduction in the standard error of the trend revision was approximately 75 80 for seasonally adjusted series The trend estimator converges faster than that of the seasonally adjusted series because trend component was stochastic while seasonal component was rather stable After 3 years 36 observations all estimators have practically converged estimators are close to 100 77 MARAVALL A 1996 DEMETRA User Demetra User Manual final version4 doc 155 DEMETRA User Manual 100 oo 9 F 8 9 9 o ge 09 9 8 ee 8 of oe oo 80 i 1 o 9 i oe eee ee eer et ia o Ly 60 o 7 9 ra o 6 7 3 E 40 a a f o O T kd Q ore eee e eg Go 0 0 5 10 15 20 25 30 4 3 2 2 4 Diagnostics H Main results Pre processing Tramo H sition Seats Seasonality tests H Spectral analysis H Revisions
100. er 7 Mark the output and click OK DEMETRA User Demetra User Manual final version4 doc 170 DEMETRA User Manual iix C ADocuments and Settings st 05s One Sheet Save calendar comected series False Csy matrix Save iregular component False Save orginal series Tue Save sa sees True Save seasonal component Tue Save trend VerticalOnentation True Folder Defines the folder that will contain the results 8 Demetrat creates the file with the output The old version of the file e g filed created in the previous period will be replaced by the new version Detailed aspects of saving the results in external files are discussed in section 4 4 5 4 4 4 Further explanations on the refreshing of multi processing In majority of cases multi processing is defined by choosing a rather general specification with numerous free options that will be used for the series This specification is called the reference specification If for some series the results are not acceptable the user will modify the reference specification to achieve a better adjustment for example by forcing the use of calendar variables In such a case the reference for the considered series becomes the specification that has been manually improved When a series is processed its estimation produces a fully identified specification which is called a point specification in the sense that it corresponds to a unique model For each series o
101. er 100014 LOS The S I ratio chart presents the final estimation of the seasonal irregular S I component and final seasonal factors for each of the period in time series months or quarters Blue curves represent the final seasonal factors and the red straight lines represent the mean seasonal factor for each period The S I ratio dots presented on the chart is modified for extreme values S I ratio values come from table D9 of X12 results see Decomposition X11 gt D tables Final seasonal factors are calculated by applying moving average to the S ratio from table D9 The results the final seasonal factors blue curves are displayed in table D102 1 15 1 1 1 05 0 9 0 65 Jan Feb Mar Apr 1995 2005 2010 27 For more details refer to LADIRAY D and QUENNEVILLE B 1999 DEMETRA User Demetra User Manual final version4 doc 92 DEMETRA User Manual You can enlarge a specific period in the S ratio chart by clicking in its zone The details are displayed in a resizable pop up window drag the right bottom corner 20000 15000 10000 5000 0 5000 10000 15000 20000 2000 1980 1985 1990 1995 2000 2005 2010 25000 The S ratio chart is a useful diagnostic tool This chart supports detection of seasonal breaks These would show up as an abrupt changes to the level of the S I ratios A seasonal break could distor
102. er to the 4 1 X12 or 4 2 TramoSeats The example below refers to X12 e Activate previously generated output from X12 e Select from menu X12DocDocxxx gt Specification gt Current Specification e Modify the span of the series in the Basic panel o Click on the Basic item in the left panel of the specification dialog box o Expand the series span node in the right panel o Choose the excluding selection type o Write 12 in the last node e Press the Apply button The processing is computed on the series without the last 12 observations A visual comparison of the forecasts of X12 and of the actual figures is displayed on the chart Specifications X12Doc 3 Pre processing Transformation E Series span z Calendar effects Selection type Regression E Arima modelling Outliers detection DEMETRA User Demetra User Manual final version4 doc 176 DEMETRA User Manual This feature is not available from Workspace menu If the user changes the currently used specification by double clicking on its name in Workspace current processing will not be re calculated The trading days regression variables can be suppressed by setting the Trading days gt Type to None in the Calendar effects panel of the specification dialog box 1 1 co S a 0 Tb o 0 4 o o 05 5 0 2 0 Basic AICC Difference 0 Transformation El Trading days pM Calendar effects Type None ynomials Regression El E
103. eries consists in removing them from the list and to re import them with the same names as previously Dynamic variables are imported by drag and drop series from a browser of the application Workspace Seasonal adjustment Variables Tools Window Help Be ees e ae E oc 2 x Xml Excel Tsw USCE Name Type Freq Start End Description is Var_1 Dynamic 12 G wr T Variables sds 4 My varables 4 i so Var l s a Var3 1000000000 i Vard ae and drop a variable 01 1950 01 1970 01 1990 01 20 01 1960 01 1980 01 2000 Names of the series can be changed by selecting a series and clicking once again when it has been selected The selected series can be displayed in a small chart window by a double click on regressor s name Dynamic variables are automatically updated each time the application is re opened Therefore it is a convenient solution for creating user defined variables 3 2 Tools menu The Tools menu is divided into tree parts e Container tools for displaying data e Tool Window charts and data transformation DEMETRA User Demetra User Manual final version4 doc 30 DEMETRA User Manual e Options different windows diagnostic and output options that can be set by user Container b F Tool Window P Options Be advised that the current implementation is not able to detect recursive processing An attempt to do so will generate a crash of Demetra The example of recursive processing is to
104. es of the series and using or not the first period for the date Options O aa XML Spreadsheet BA a H Diagnostics El Outputs BeainPeriod Use the first period for the date O OK Cancel Diagnostic This part includes information about the chosen significance level used by Demetra for an evaluation of the performed seasonal adjustment The default settings for the tests displayed in this section can be changed by the user Options eee Default SA processing outpu ri Browsers 5 Formatters Diagnostics 2 Visual spectral analysis ctral resid ity DEMETRA User Demetra User Manual final version4 doc 40 DEMETRA User Manual For the spectral analysis the following settings are also included threshold for identification of peaks number of years at the end of the series considered in the spectral analysis checking if the spectral peak appears on both SA series and irregular component Outputs This section enables to specify which output s items will be saved and folder in which Demetra saves the results It is possible to save the results in the following formats txt xls csv or send them to the database by ODBC TXT With the txt format the user can define the folder that will contain the results and the components that will be saved XLS In addition to the options available for txt format using xls format the user can specif
105. es p Skewness Kurtosis Normality ndence of the residuals Ljung Box 24 0 5164 Box Pierce 24 Drei Ljung Box on seasonality 3 Up and Down runs number Up and Down runs length DEMETRA User Demetra User Manual final version4 doc 100 DEMETRA User Manual Coo Ljung Box on squared residuals 24 0 0028 Box Pierce on squared residuale 24 0 0054 For each test corresponding p value is reported The p value is the probability of obtaining a test Statistic at least as extreme as the one that was actually observed Green p value means Good yellow means Uncertain and red means Bad In the example above for tests one to three the null hypothesis was accepted p values higher than 5 It means that it can be assumed that residuals are independent and random They are approximately normally distributed The p value marked in red indicates that the null hypothesis was rejected Linearity of the residuals test provides an evidence of autocorrelation in residuals A linear structure is left in the residuals Demetra also presents a distribution of the residuals In this section autocorrelation and partial autocorrelation functions as well as histogram graphics of residuals estimated from RegArima model are presented Autocorrelations 06 i pri l 0 2 0 3 0 2 0 1 4 3 2 1 3 Decomposition This part includes tables with results from consecutive iterations of X 11 algorithm and quality measures D
106. eseccceeecccecsceeecsseeneeeeenseeeueceseueceeseseneueseneueeees 12 A Fa TVS CAVA Benea sere tcerosnssaccratencewan on aesnncasacem ses eecawsosssaanucavicuteuscacewatstaavsnateeuone saverenwier 12 Eo FM SY a aN 12 To ClO nE Deme P aaocssetectucneseneteavsne ie 12 2 Mam AD DIC ATION S WINdOWS essene nee isanntcaadencsbaunaneeoeatonnes 13 2 1 Overview Of the SoftWare cccccccsssssssseeccccccceeesseeccccesesseuesseeeecesssauuesseeceessaeasseeceecesssaeagseess 13 De OW SCs cece ees ase orig heise oc ei enue ase eases onto aac ete acess natenet a esenese eet 15 De VS PROMS UC Siprccrreacansearcusestetoeavievodac avian S 19 De WN OMIKS DCO eras ats soiea Sse seas otde et onttee 2 oneew cea daica se astiecedentvig seeder ceva sneeeedenicie tesee og ee anoneatsn cote teas tate des 19 Pigs OR acnnte venous sutasicssunaes cance saceieryachapesntasinea esiournteqacted our con sanura satin baoueestuyaonnis ciaueyesaswsaeaaeeceesonsieeraek 21 ZO ARESUN SG TIVO cetanesenanescectesaesscecohene ea cgatecesu sone co sees aaeduosencnceasae te sen esoasena o aaecaseaeanaooateneanesasneecesease 22 Be POD ICALIOND S MENU secina E E S 24 Sl WOK P 6 NEN e er nn ce nee eee ae 24 cay We LE ee E ee 23 3 1 2 User defined regression Variables ccccccsccssccssccssceescesccesccesscuscessesscesseesceuscens 29 TOOR WMI a E E E E T A E E 30 i eae gam CORINE e E ern E eee een eet eee 31 D2 2c TOO WIMGOW EE E A E 34 sR SSASOMAC Ha E E E E E seeom avtreatver
107. esidual seasonality diagnostics The residual seasonality diagnostics implemented in Demetra correspond to the set of tests developed in X12 One of them is F test on stable seasonality see the Annex section 12A which is computed on the differences of the seasonally adjusted series component CSA see above and on the irregular component component Cl see above In order to extract the trend from the monthly time series a first order difference of lag three is applied a first order difference of lag one in the other cases For the seasonally adjusted series it is tested if residual seasonality is present Test is performed twice on the complete time span and on the last 3 years span Results of the test Pr F gt val Demetra default setting 0 01 0 05 Bad 0 05 0 1 e Number of outliers A high number of outliers indicates that there is a problem related to a weak stability of the process or the reliability of the data is low If the high number of outliers has been detected above 3 according to the table the chosen Arima model cannot fit all of the observations Results of the test Treshold Demetra default setting 0 05 0 1 Bad 0 03 0 05 36 DAGUM E B 1987 DEMETRA User Demetra User Manual final version4 doc 109 DEMETRA User Manual e M statistics For the test results refer to 4 3 2 1 3 Seasonality tests Main results Pre processing Reg Arima Decomposition 411 D
108. f a multi processing the software stores the reference specification and the point specification in an xml file When a user wants to refresh a processing one has to define for the updated series the specifications called estimation specification that will be used Following the refreshing option Demetra removes some constraints of the point specification in the limits of the reference specification For example when the All outliers option is selected any automatically identified outliers is removed and the automatic outliers identification option of the reference specification is used If that reference specification doesn t allow automatic outliers identification the estimation specification will not allow either Without such an approach it would be difficult to define exactly the specification that should be used when a processing is refreshed DEMETRA User Demetra User Manual final version4 doc 171 DEMETRA User Manual The list of the constraints that are removed from the point specifications following the refreshing options is presented below the second column should be interpreted as a cumulative list Option Removed constrains All outliers Re estimation of all the outliers Arima and outliers Re estimation of the whole Arima model Concurrent adjustment The reference spec is used Considering the way Demetra works it is clear that the reference specification should be chosen as general as possible Otherwis
109. fining a multi processing 1 Creation of a new multi processing This option opens the following window iol x Method Estimation Processing Priority Quality Warnings Computed 12 1899 01 1900 New processing 0 item The user should first activate the specification and then drag and drop the time series into the window We recall that the active specification can be selected in the workspace through a local menu it can be either a pre defined specification or a user defined one If there is no active specification in the Workspace panel the user is unable to drag and drop time series into specification window The user can change initial choice of the active specification and choose other specification for next set of series This option enables to launch the seasonal adjustment for one time series using DEMETRA User Demetra User Manual final version4 doc 157 DEMETRA User Manual different specifications in order to compare the results The picture below presents multiprocessing in which four different specifications has been used Processing Summary Matroc view Method Estimation Processing Priority Quality Warnings Computed TS RSA3 Concument Unemployment Sold production of industry TS RSA3 Concurrent Valid Severe E CPI CAPITAL CITY TS RSA5 Concurent Valid Severe ff CRUDE PETROLEUM F TS RSA5 Concurrent Valid EXPORTS FOB 12 RSA3 Concurent Valid IMPORTS CIF
110. hat yet BE if j k Oif j k t 1 and Y cos 4t Ysin 4t A t t 1 2 2 so that IC A and i A are uncorrelated N 0 1 random variables n n Test on the periodogram Under the hypothesis that z is a Gaussian white noise and considering subset J of Fourier t frequencies we have i J lout AA S Pa ae jeJ If we consider the sets of Fourier frequencies on or near the trading days frequencies on one side and on or near the seasonal frequencies on the other side we can use the above formula as rough test regarding the absence of trading days seasonal effects in the considered series The software considers the Fourier frequencies which are on or near the following frequencies the nearest is chosen or two if they are equidistant Annual frequency Trading days 27 12 47 12 67 12 87 12 127 12 d 2 714 Ce m6 ao oS Ao 1 292 1 850 2 128 where d is computed as follows if s is the frequency of the series DEMETRA User Demetra User Manual final version4 doc 195 DEMETRA User Manual 365 25 n d n modulo 7 Autoregressive spectrum Autoregressive spectrum estimator is defined as follows A AN ra A 101 m S 4 aT mao p J 2r X j Pa j l where frequency 0 lt lt 0 5 the sample variance of the residuals A coefficients from regression x x on x x 15 j lt m Visual spectral analysis A A A Criterion of visual
111. he average of the defined diagnostics Bad 1 Uncertain 2 Good 3 is lt 1 5 No Error no Severe diagnostics the average of the defined diagnostics Bad 1 Uncertain 2 Good 3 is in 1 5 2 5 Good No Error no Severe diagnostics the average of the defined diagnostics Bad 1 Uncertain 2 Good 3 is gt 2 5 According to the table Error and Severe diagnostics are absorbent results The quality of each diagnostics except for Undefined and Error can be parameterized by the user in Tools gt Options gt Diagnostic menu 4 3 2 1 X12 For X12 the basic output structure is as follows e Main results o Charts o Table o S I ratio e Pre processing RegArima o Pre adjustment series o Arima o Regressors o Residulas e Decomposition X 11 o A Tables o B Tables DEMETRA User Demetra User Manual final version4 doc 88 DEMETRA User Manual o C Tables o D Tables o E tables o Quality measures e Diagnostics o Seasonality tests Oo Spectral analysis o Revisions history o Sliding spans o Model stability Detailed description of the seasonal adjustment outcomes is presented below 4 3 2 1 1 Main results The Main results node includes basic information about pre processing and the quality of the outcomes z Charts Table be S ratio H Pre processing RegAnma H Decomposition 411 E Diagnostics The first section summarises
112. he expense of the speed of the processing and for results that are usually very similar Diagnostics pe Seasonality tests H Spectral analysis Revisions history B Revisionpolig a Parameters H Siding spa Visible Nodes Outliers In the revisions history panels a complete overview of the different revisions for a given time span can be obtained by selecting with the mouse just like for zooming the considered periods The successive estimations are displayed in a separate pop up window DEMETRA User Demetra User Manual final version4 doc 116 DEMETRA User Manual 2 CSA first estimations 07 2005 06 2005 11 2005 04 2006 09 2006 O02 09 2005 01 2006 05 2006 09 2006 EE 2006 00 11 2005 03 2006 07 2006 11 200 0 162 0 February 0 163 0 061 UUs 0 141 AEE June August 0 108 ee 0 01 Fi Edit gt Export Copy all Print Remove Legend Remove all Settings Paste DEMETRA User Demetra User Manual final version4 doc 117 DEMETRA User Manual One can also get all the revisions for a specific period by clicking on the point that corresponds to the first estimate for that period The results of those pop up windows can be copied or dragged and dropped to other software e g Excel G nail lete Format aga Sort amp a Y 7 cs Clear a Filter Editing Q R CSA 2 1993 Revisions 2 1 1993 122 6861 3 1 1993 122 4878 4 1 1993 122 26
113. he user Adds the processing to the Workspace Once the output was created the user can save the multiprocessing The appropriate item will appear in the workspace tree The user can add new time series to the multi processing using Edit gt Add items option SAProcessing 2 Update reports Edit Add items Priority a Paste Generate output Add to workspace Initial order Option Edit gt Paste enables to add to the existing multi processing a new time series directly from external source e g Excel Before choosing this option the user should copy the time series data name of the time series and dates Otherwise the following message is displayed Eal work Eli Single processing 3 vee gt Tramo Seats E gt x12 Xe Elie Multiprocessing Unabled to paste data ame eg 2 Processing 2 Saved H Specifications fa Calendars A User defined variables 4 4 2 3 Detailed results and modification of the specification For each time series from multi processing seasonal adjustment Demetra offers the access to the complete description of the results by a double click on the time series name This option is available for both Processing and Matrix view panels The user is allowed to modify the specification by changing the options in the left part of the window This option could be useful in case the quality of a specific processing is low and the user wishes to modify some options to get a better res
114. hema Excel TSW USCB Text and ODBC The installation procedure has copied several files in different formats in the subfolders of My Documents Data The method of opening Excel workbooks is presented below The procedure is similar for the other providers 1 Click on the Excel tab of the browsers panel 2 Click on the left button see below 3 Choose an Excel workbook for instance INSEE xlsx see screen below DEMETRA User Demetra User Manual final version4 doc 15 DEMETRA User Manual Demetra pE E Oj x Workspace Seasonal adjustment Tools Window Help Browsers y K eee a x sei Eos aT x 2011 05 02 01 05 Folder plikow 2011 05 02 01 06 Folder plik w 2011 03 31 21 31 Arkusz progr Final nodes of the trees represent time series and their parents represent collections of time series Those nodes correspond with spreadsheets names Different browsers show the data in trees that can be expanded by double clicking their nodes or single clicking the signs The tree shows not only how the time series were organized in Excel s workbook but also how many series are in the whole workbook and in each particular spreadsheet DEMETRA User Demetra User Manual final version4 doc 16 DEMETRA User Manual Xml Excel Tsw usce total number of time series in a workbook list of time series in the spreadsheet sa INDUSTRIAL PRODUCTION e MINING PRODUCTION s EXPORTS s
115. heoretical spectrum of the stationary and non stationary model and autocorrelation function of the stationary part of the model In the top left part an infinite sample spectrum graphic is displayed The blue line represents the Arima model identified by regArima In the top right part an auto correlation graph corresponding to the Arima model is presented In the bottom part estimated coefficients of parameters regular and seasonal AR and MA are shown in closed form i e using the backshift operator B In this part frequencies corresponding to regular AR parameters are also reported if they are present 0 Pli2 FI 10 20 30 Polynomials regular AR 1 0 34299 B 0 32833 B42 seasonal AR 1 regular MA 1 seasonal MA 1 0 35933 5 Frequency of the regular AR roots 3 14159265358979 Regressors This section presents all deterministic regressors used by RegArima part including trading days variables leap year effect outliers Easter effect ramps intervention variables user defined variables Friday Saturday AO 11 1964 AO 2 1975 AO 6 2004 1LS 11 2008 lt 0 2 Pre processing RegArima Pre adjustment series Arima Regressors i oA Residuals Decomposition X11 Diagnostics Olo a ulo a ujolo O a ced ae ead eee ae s Olsiaioioiscio c ecco cco ooooooooo ooooooooo i i i i i me i it et et 4 DEMETRA User Demetra
116. hile seasonal peaks light blue are quite wide especially the fourth and fifth indicating large amount of stochastic seasonality As a result seasonally adjusted spectra dark blue and spectra of transitory component green include peak which is an evidence of residual trading days effect DEMETRA User Demetra User Manual final version4 doc 143 DEMETRA User Manual Trend Cycle Seasonally adjusted Seasonal Transitory Irregular Spectrum ACGF stationary Second panel shows ACGF stationary function Values of the ACGF function are autocorrelation coefficients of stationary inducing transformation of components They are theoretical values i e they are not computed on the data 0 5 o o m I 0 Ho e e aaa a a a a i o m o m z o oda 0 5 5 DEMETRA User Demetra User Manual final version4 doc 144 DEMETRA User Manual e Final estimators H Main results H Pre processing Tramo Decomposition Seats Stochastic series Model based tests WK analysis _ Errors an alysis Ee Diagnostics TramoSeats uses seasonal adjustment filters to compute the values of different time series components The convergence of these symmetric filters requires past and future time series observations which are not available at the beginning and end of the time series Hence one needs to extend the time series from both ends calculate forecasts and backcasts to be able to use the filter This is
117. history H Sliding spans H Model stability For TramoSeats Demetra calculates the following statistics o Friedman test o Kruskal Wallis test o Test for the presence of seasonality assuming stability o Evaluative seasonal test o Residual seasonality test o Combined seasonality test Qa g P z 35 In the Diagnostic section the user will find also Spectral analysis Revisions history Sliding spans Model stability For details please refer to Seasonal adjustment results for X12 and to the Annex Description of the results and options available in Diagnostic section are presented in X12 DEMETRA User Demetra User Manual final version4 doc 156 DEMETRA User Manual 4 4 Multi processing Multi processing specification is designed for quick and efficient seasonal adjustment of large data sets Multi processing specifications that mix different seasonal adjustment methods are available The software provides two different ways to perform multi processing The first solution is based on the active specification in that solution the series that are subject to ina multi processing are automatically associated with the active specification The second solution consists in using a wizard which allows the users to associate series and specifications step by step Both functions are activated from the main menu Seasonal adjustment iF Specifications i ia Single analysis b New ra Wizard 4 4 1 De
118. iagnostics H Spectral analysis H Revisions history H Sliding spans H Model stability The diagnostic node includes the set of seasonality tests useful for checking the presence of seasonality in time series Those tests are described in the Annex section 12A The exemplary results from Demetra are discussed below All tests have been calculated for the same time series e Friedman test The seasonal component includes the intra year variation that is repeated each year stable seasonality or evolving from year to year moving seasonality To determine if stable seasonality is present in a series Demetra computes the Friedman test using the seasons months or quarters as the factors on the preliminary estimation of the unmodified S I component Fnedman test Friedman statistic 73 4321 Distribution F stat with 11 degrees of freedom in the numerator and 154 degrees of freedom in the denominator P Value 0 0000 Stable seasonality present at the 1 per cent level A high test statistics and low significance level indicates that a significant amount of variation in the S I ratios is due to months or quarters respectively which in turn is evidence of seasonality If the p value is lower than 0 1 the null hypothesis of no seasonal effect is rejected Conversely a small value of the F test and high significance level close to 1 0 is evidence that variation due to month or quarter could be due random error and the null hypothesi
119. ial series Q Results of the test lt 0 000001 gt 0 000001 o Annual totals The test compares the annual totals of the original series and those of the seasonally adjusted series The maximum of their absolute differences is computed and related to the Euclidean norm of the initial series Results of the test agnostic J0 1 0 5 J0 05 0 1 J0 01 0 05 e Visual spectral analysis Demetra identifies spectral peaks in seasonal ad trading days components using an empirical criterion of visual significance For more information see the Annex section 9A e RegArima Residuals diagnostics DEMETRA User Demetra User Manual final version4 doc 107 DEMETRA User Manual Several tests are computed on the residuals of the RegArima model The exact definition of what we mean by residuals should be clarified Indeed X12 and Tramo are based on different estimation procedures of the likelihood of the RegArima models which lead to different residuals Demetra takes another way similar to the solution developed in Stamp for instance The Annex section 1A describes those solutions In most cases the different sets of residuals yield slightly different diagnostics However their global messages are nearly always very similar o Normality test The joint normality test which combines skewness and kurtosis tests is the Doornik Hansen test see the Annex section 12A which is distributed as a ye Re
120. iance 1 0000 trend Non stationary AR 1 28 B 2 Stationary AR 1 MA 1 0 059791 B 0 94021 B 2 Innovation variance 0 0465 seasonal Non stationary AR 1 B B24 B 3 644 6 5 86 BT 86 B9 B 10 B11 Stationary AR 1 MA 1 13862 B 1 1023 B 2 1 1469 B 3 1 0739 B 4 0 81941 B 5 0 62326 B 6 0 41212 B 7 0 25791 B 8 0 024671 B 9 0 01917 B 10 0 15503 B 11 Innovation variance 0 1110 transitory Non stationary AR 1 Stationary AR 1 0 36007 B 0 3327 B 2 MA 1 0 50781 B 0 49219 B 2 Innovation variance 0 0571 irregular Non stationary AR 1 Stationary AR 1 MA 1 Innovation variance 0 1454 Stochastic series H Main results H Pre processing Tramo El Decomposition Seats Model based tests E WK analysis E Diagnostics This part presents the table containing the following series produced by Seats e Seasonally adjusted series e Trend e Seasonal component e Irregular component contains transitory component if any e Trend forecasts for 2 years DEMETRA User Demetra User Manual final version4 doc 136 DEMETRA User Manual e Seasonal component forecasts for 2 years Model based tests Main results H Pre processing Tramo Decomposition Seats Stochastic series z Model based tests E WK analysis ak Diagnostics Model based tests concentrate on distribution of components theoretical estimators and empirical estimates stationar
121. icted with regard to their original implementations For this reason there are some differences between original programs and programs implemented in Demetra The aim was to develop the software which enables the comparison of the result from TramoSeats and X 12 Arima For this reason the revision history and the sliding spans analysis are available in Demetrat both for TramoSeats and X 12 Arima On the contrary some functionalities implemented in original programs are missing in Demetrat e g using X 12 Arima under Demetrat it is not possible to do a pre adjustment of the original series with prior adjustment factors to specify Arima model p d qg P D Q without some lags in the regular part is not possible for the X 12 part in Demetra The User Manual is divided into five parts Chapter 1 presents the general features of the software In Chapter 2 the application s menu is outlined Chapter 3 focuses on the workspace menu and useful options offered by Demetra Chapter 4 describes how to define the seasonal adjustment of a single series and large sets of series The X 12 Arima and TramoSeats specifications are presented In this part the results of seasonal adjustment as well as their interpretation is discussed Some theoretical aspects of seasonal adjustment using X 12 Arima and TramoSeats are also included 3 For example the user cannot specify the model 2 1 1 0 1 1 without parameter AR 1 DEMETRA User Demetra User M
122. ies which appear in the results window X12 or TramoSeats can be dragged and dropped to any other window of the Tools menu It is also possible to drag and drop the results in the item chosen from container l0l x X12 RSA4c Source XCLPRVDR Name Industries alimentaires 001563038 E Main results fe ian feb a apr may jun a a sep oct mv E Pre processing RegAvima 1990 90 1759 90 531 90 7935 91 0339 91 1342 91 Pre adiustment series B4 1991 91 727 92 1036 92 3993 925969 92 8775 93 0494 93 0101 92 9564 92 8958 92 8929 92 9923 93 Aima mn 1992 93 1416 93 2938 93 6028 93 7782 93 7544 93 9555 93 9261 93 7982 93 6618 93 4079 93 1276 92 Regressors B7 1993 92 6473 92 365 92 1184 92 036 91 9859 91 9647 92 0916 92 2279 92 3067 92 3454 92 4593 92 Residuals BS N4994 92 7179 92 9295 92 9943 93 0468 93 2266 93 2663 93 2749 93 4096 93 5665 93 8244 94 0728 94 Statistics ni 199 94 3763 94 472 94 7609 95 1125 95 3431 95 6214 95 8509 95 9689 96 1102 96 2225 96 2902 9 Distribution B11 1996 96 7442 97 1059 97 4285 97 6739 97 8944 98 0751 98 2278 98 405 98 526 98 7485 99 0255 99 El Decomposition X11 tae 1997 92784 99 0939 99 0633 99 1356 99 4343 99 7614 100 061 100 201 100 346 100 463 100 447 10 ATables B20 1998 100 9 101 103 101 469 101 634 101 56 101 444 101 325 101 265 101 267 101 128 101 048 10 B Tables 1999 101 077 Q0 948 100 824 101 008 101 273 101 313 101 314 101 274 101 21 101 26 101
123. iews e Trading Days seven regression variables which correspond to differences in economical activity between all days of the week and leap year effect e Working Days two regression variables which correspond to differences in economical activity between the working days Monday to Friday and non working days Saturday Sunday and the leap year effect e None one regression variable which corresponds to the leap year effect This window should be used to analyze the data created by the calendar Actually Demetrat enables the user to include exclude the leap year effect from the seasonal adjustment model see 4 1 3 1 and 4 2 2 1 The series can be copied by drag and drop as it is shown in the picture below The local menu can be used to copy and paste the series to other applications e g Excel DEMETRA User Demetra User Manual final version4 doc 28 DEMETRA User Manual Lle click on header to paste one variable to the browser click on the top left corner cell to paste all variables to the browser i mn aa e et et l aal ol etl el et oe O a aes 5 5 OOGG fa oe 82 fF oO B88 gt z Calendars defined by the user are added to the Workspace tree The user can display edit or add new calendar by clicking on Calendars in Workspace tree and choosing appropriate option from the pop up menu for more details see 2 4 Workspace 3 1 2 User defined regression variables User defined regression
124. ifference in detecting turning points between original and seasonally adjusted data or trend cycle _in terms of period month or quarter The phase effect function is calculated separately for seasonally adjusted series red line and trend cycle blue line As a rule phase effect has a positive value which means that seasonally adjusted series and trend cycle shows turning points later than original time series This delay is undesired featured of seasonally adjusted time series and is regarded as a drawback by statisticians who use seasonally adjusted data for modeling and forecasting For this reason it is expected that phase delay is zero or nearly zero The phase effect is measured in number of periods horizontal axis Vertical axis presents range of frequencies of cyclical interests Frequencies close to O indicate long term Pi trend while is a 2 year cycle Hence for monthly time series presented below in seasonally adjusted data estimator induces high phase delay for the long term and short term cycle approximately 3 months while for the 2 year cycle phase delay is a bit smaller 2 moths DEMETRA User Demetra User Manual final version4 doc 151 DEMETRA User Manual Square gain function 6 Phase effect i PI12 PI6 e WK filters Preliminary component estimator will imply the one sided asymmetric WK filter see aforementioned description of the WK filter and because of that will be adversely affected by phase
125. ification Others Arima Arima modelling dimension parameters fixed parameters Outliers detection Others Outliers Automatic outliers detection others model Seats parameters ES 2 2 Transformation Comments Oom Fa spec Series span Span used for the processing The span can be computed dynamically on the series for instance Last 90 obs Function Arima model Transformation of data logarithm level none Others or log level pretest Arima model Control of the bias in the log level pretest the Others function is active if Function Auto fct gt 1 favors levels fct lt 1 favors logs DEMETRA User Demetra User Manual final version4 doc 67 4 2 3 Trading days gt Trading days gt Details gt Trading days option is available if Trading days Predefined DEMETRA User Manual O Sees span Selection type Function Fet Calendar effects E Arima modelling Outliers detection Estimation Decomposition Seats Fet Fct Controls the bias in the log level pretest Fet gt 1 favors levels Fet lt 1 favors logs Calendar effects Individual spec Others TradingDay Easter Effect regression variables DEMETRA User Demetra User Manual final version4 doc Comments The user can choose between e None Predefined Calendar UserDefined None means that calendar effects will not be included in the regression Predefined means that default calendar w
126. ill be used Calendar corresponds to the pre defined trading days variables modified to take into account specific holidays It means that the user should specify the type of trading days effect td1 td2 td6 or td7 and chose calendar which will be used for holidays estimation UserDefined is used when the user wants to specify in a free way his own trading day variables With this option the calendar effect is captured only by regression variables chosen by user from the previously created User defined variables see 3 1 2 Acceptable values td1 includes the weekday weekend contrast variable td2 includes the weekday weekend contrast variable and a leap year effect td6 includes the six day of the week variables 68 DEMETRA User Manual TramoSeats Comments Individual spec Argument or Calendar td7 includes the six day of the week variables and a leap year effect Trading days gt Others Pretest of the trading days correction Pretest TradingDay Easter Option available for type Predefined Effect Trading days gt Others ireg regeff When the user chooses the calendar type Details gt iuser ilong for the trading days the corresponding Holidays nser holidays should be specified It should be noted that such a holiday must have been option i previously defined see 3 1 1 available Trading days Calendar type Trading days gt Others ireg regeff When the user chooses f
127. ima coefficients used for final test of model parsimony ReduceCV automdl reducecv The percentage by which the outlier critical value will be reduced when an identical model is found to have a Ljung Box statistic with an unacceptable confidence coefficient Reduce SE Percentage reduction of SE Unit root limit Unit root limit for final model Should be gt 1 13 According to GOMEZ V and MARAVALL A 2001 the Hannan Rissanen method is a penalty function method based on BIC Bayesian Information Criterion where the estimates of ARMA model parameters are computed by means of linear regressions These estimates are computationally cheap and have similar properties to those obtained by Maximum Likelihood 14 Cancellation problem is presented in the Annex Chapter 7A DEMETRA User Demetra User Manual final version4 doc 59 DEMETRA User Manual Ba Mixed x Transformation Ljung Box Limit i Calendar effects 2 Advanced Regression Balanced HR initial Initial unit root limit Final unit root limit Arma Limit ReduceCV balanced Controls whether the automatic model procedure will have gt a preference for balanced models 4 1 7 Arima Options included in this section are active only if IsEnabled parameter from Automatic modeling section is set to false In this window the user can specify the parameters of Arima model manually by setting P D Q BP BD BQ values The estimation of parameters value is iterativ
128. initial seasonal factors in each iteration and a 3x5 moving average to calculate the final seasonal factor Misr automatic choice of seasonal filter The seasonal filters can be selected for the entire series or for a particular month or quarter Details on x11 unavailable Enable to assign different seasonal filter for each seasonal filters period Option is active if seasonalma Mixed List of available options is the same as for Seasonal filter item apart from Mixed option Automatic x11 trendma Automatic selection of the Henderson filter is Henderson used when the corresponding item is selected filter Otherwise the length given by the user is used True 7 Term true7term Specifies the end weights used for the seven term Henderson filter Calendar calendarsig Specifies if standard errors used for extreme Sigma values detection and adjustment are computed separately for each calendar period month quarter or separately for two complementary sets of calendar periods 18 X 12 ARIMA Reference Manual 2007 19 LADIRAY D and QUENNEVILLE pg 1999 DEMETRA User Demetra User Manual final version4 doc 65 DEMETRA User Manual Individual Argument Comments spec Sigma Vector x11 unavailable Specifies one of the two groups of periods for whose irregulars a group standard error will be calculated under the calendarsigma Select option Specifications X12Doc 10 X Basic El 0 Basic
129. ion of regression models with missing observations and Arima errors in the presence of possibly several types of outliers Seats Signal Extraction in Arima Time Series performs an Arima based decomposition of an observed time series into unobserved components Both programs are supported by Bank of Spain for more details see GOMEZ V and MARAVALL A 2001 or CAPORELLO G and MARAVALL A 2004 2 X 12 Arima is a seasonal adjustment program developed by the US Census Bureau It includes all the capabilities of the X 112 program which estimates trend and seasonal component using moving averages X 12 Arima offers useful enhancements including extend the time series with forecasts and backcasts from Arima models prior to seasonal adjustment adjustment for effects estimated with user defined regressors additional seasonal and trend filter options alternative seasonal trend irregular decomposition additional diagnostic of the quality and stability of the adjustments extensive time series modelling and model selection capabilities for linear regression models with Arima errors X 12 Arima is supported by the US Bureau of Census for more details see FINDLEY D F MONSELL B C BELL W R OTTO M C CHEN B C 1998 DEMETRA User Demetra User Manual final version4 doc 7 DEMETRA User Manual some ESS Guidelines were not easy to apply using Demetra software The only effective long term solution was to create new seasonal adjustme
130. k on the series of the browsers or by dragging dropping the series in the left panel of the single processing window 2 bythe main menu Other method to define single seasonal adjustment is to use the New option from the main menu Seasonal adjustment i Specifications Multi processing Wizard Demetra will display a new single processing window with the active specification the one which is ticked in the Workspace panel DEMETRA User Demetra User Manual final version4 doc 81 DEMETRA User Manual In the next step click Choose the method from the left hand list and mark TramoSeats or X12 Then choose the specification from the list of specifications the contents of the list depends on the method chosen or define the new one Demetra displays the window with the chosen specification The last step is to drag the time series from the browser and drop it in this window The seasonal adjustment process is started instantly and the output is displayed in the screen 4 3 1 2 Creation of a single processing by defining new specifications 1 by Wizard This function is activated from the main menu Lu Specifications DEMETRA User Demetra User Manual final version4 doc 82 DEMETRA User Manual In the first step the user should choose the series one wants to analyse using the browser Single analysis Wizard xj Choose a series Xml Excel Tsw usce Choose a method New data set od
131. l identification Ub1 Arima model Initial unit root limit in the automatic Unit roots differencing procedure Ub1 is advanced and rarely used option used in the detection of DEMETRA User Demetra User Manual final version4 doc 74 DEMETRA User Manual Comments tem aaa spec unit roots in Tramo It is is used as a threshold to detect unit roots in the first step of the automatic identification of the differencing polynomial which consists in the estimation of a 2 0 0 0 0 plus mean Arma model Arima model ub2 Final unit root limit in the automatic Unit roots differencing procedure Ub2 is advanced and rarely used option used in the detection of unit roots in Tramo It is used in the next steps of estimating procedure based on the estimation of 1 d D 1 bd 0 plus mean Arma models Others pcr Ljung Box Q statistic limit for the acceptance Automatic of a model model identification Others Minimum t for significant mean Automatic model identification Transtormation s enabled r effects Regression a Aima modelling 4 2 6 Arima model Options included in this section are active only if IsEnabled parameter from Automatic modeling section is set to false 23 Cancellation issue is described in the Annex Chapter7A DEMETRA User Demetra User Manual final version4 doc 75 DEMETRA User Manual T Comments Individual spec Mean Arima model imean It is considered that the mean a con
132. liers are simple forms of intervention variables Ramps Others others ireg ilong Ramp effect means a linear increase or delta iseg decrease in the level of the series over a regeff specified time interval from ft to It is modeled by regression variable l fort St RP t t t t 1 fort lt t lt t O fort2t All dates of the ramps must occur within the time series Ramps can overlap other ramps additive and level shifts outliers Intervention Others others ireg nser The intervention variables are special events variables ilong deltas known a priori strikes devaluations political idids iseg evens and so on Intervention variables are regeff modeled as any possible sequence of ones and zeros on which some operators may be applied This option enables the user to define four types of intervention variables e Dummy variables e Any possible sequence of ones and Zeros of any sequence of ones and i 1 B zeros 0 lt 0 Delta lt 1 of any sequence of ones 1 5 B and zeros 0 lt DeltaS lt 1 User defined Others others ireg iuser The user defined variables effect can be variables nser regeff assigned to the trend irregular holiday or can exist as an additional component option Undefined For practical considerations seasonal effects are currently not supported The user can specify the structure of the lags When regression variable Var is in
133. line depends on the width of the seasonal peaks in the seasonal component estimator spectrum navy blue lines 0 8 j 0 6 0 4 0 2 0 Pli2 FI e Squared gain of components filter The squared gain controls the extent in which a movement of particular amplitude at a frequency is delivered to the output series It determines how the variance of the series contributes to the variance of the component for the different frequencies In other words it specifies which frequencies will contribute to the signal that is it filters the spectrum of the series by frequencies If squared gain is zero in band it means that the output series is free of movements in this range of frequencies On the contrary if for some square gain is 1 then all variation is passed on to the component estimator The figure below points out that seasonal frequencies are assigned to the seasonal component while the seasonally adjusted series captures the variance of the non seasonal part of the series As a consequence it is expected that seasonal component estimator captures only the seasonal frequencies so its peaks assume unitary values at the latter frequencies On the contrary estimator of the nonseasonal part of the time series is expected to eliminate seasonal frequencies leaving unmodified non seasonal frequencies Therefore squared gain of seasonally adjusted data should be nearly one apart from seasonal frequencies In the
134. lysis with Applications to Economic and Environmental Problems Journal of the American Statistical Association No 70 CAPORELLO G and MARAVALL A 2004 Program TSW Revised Reference Manual Banco de Espana http www bde es servicio software tramo tswrm pdf DAGUM E B 1987 Modelling Forecasting and Seasonally Adjusting Economic Time Series with the X 11 ARIMA Method Journal of the Royal Statistical Society Series D The Statistician Vol 27 No 3 4 DAGUM E B 1979 On the Seasonal Adjustment of economic Time Series Aggregates A Case Study of the Unemployment Rate Counting the Labor Force National Commission Employment and Unemployment Statistics Appendix 2 317 344 Washington DURBIN J and KOOPMAN S J 2001 Time Series Analysis by State Space Methods Oxford University Press 2000 Seasonal Adjustment of Monetary Aggregates and HICP for the Euro Area ECB August 2000 http www ecb int pub pdf other sama0008en pdf FINDLEY D and MARTIN D 2006 Frequency Domain Analyses of SEATS and X 11 12 ARIMA Seasonal Adjustment Filters for Short and Moderate Length Time Series Journal of Official Statistics Vol 22 No 1 2006 pp 1 34 FINDLEY D F MONSELL B C BELL W R OTTO M C and CHEN B C 1998 New Capabilities and Methods of the X 12 ARIMA Seasonal Adjustment Program Journal of Business and Economic Statistics 2 16 127 152 FIND
135. mation while keeping the user in the same window e Tabbed arranges all windows in central zone as tabs e Tile vertically arranges all windows in central zone vertically e Tile horizontally arranges all windows in central zone vertically e Skinning allows to custom graphical appearance of Demetra e Documents e List of windows names currently displayed in the central panel This list is dynamically updated when the user opens close some windows On the example below four items are available The one which is active is marked dw Hl I Seating CESE E Tabbed Tile vertically salta Method Estimation Processing Priority Quality Wamings D Daa KP TramoSeatsDoc 2 Skinning TS Source XCLPRVDR Name Dwellings competed 1 SAPr essit P Main resus Pre processina Tramo EEEE okati E Chart p loj xj 2 TramoSeatsDoc 2 l g a er Dec 45000 40000 e 35000 30000 tick indicates which 00 window is active now 20000 As an example the following chart presents the comparison of the results for Tile horizontally option DEMETRA User Demetra User Manual final version4 doc 46 DEMETRA User Manual X12Doc 12 Tools Window Help ce XCLPRVDR Name IMPORTS VOLUME TOTAL INDEX NSA Tile vertic Tile horizontally Skinning 1 X12Doc 12 2 TramoSeatsDoc 9 Documents 1 MacOS 2 Office 2007 Black 3 Office 2007 Bl
136. metra could be different that ones obtained from other software in which X12 Arima and TramoSeats methods are implemented e g SAS TSW USCB The definition of the residuals can be found in these references ANSLEY C F 1979 GOMEZ V and MARAVALL A 1994 LJUNG G M and BOX G E P 1979 OTTO M C BELL W R and BURMAN J P 1987 Least squares estimation by means of the QR decomposition ZA Least squares estimation by means of the QR decomposition We consider the regression model y XP eE The least squares problem consists in minimizing the quantity I X8 y 5 Provided that the regression variables are independent it is possible to find an orthogonal matrix Q so that R Q X o where R is upper triangular We have now to minimize o o R8 a I2 Ilb 1 2 OxB Qy where QY o x1 4 and Qy 1 The minimum of the previous norm is obtained by setting G R a In that case Il RG all 0 2 DEMETRA User Demetra User Manual final version4 doc 180 DEMETRA User Manual The residuals obtained by that procedure are then D as defined above It should be noted that the QR factorization is not unique and that the final residuals also depend on the order of the regression variables the columns of X 3A Specifications RSAO Level Airline model RSA1 Log level outliers detection Airline model TramoSeats ae Log level working days Easter outliers detection Airlin
137. modify existing one The list on the left contains all national calendars defined by the user In the panel on the right the user could specify the successive parameters National calendar Calendar_1 Pre specitied holidays Easter related days Fed days In the example below it is shown how to define fixed holidays choosing the month from the list and specifying the appropriate day of the month If the validity period hasn t been specified the regressor will be applied for all time series span DEMETRA User Demetra User Manual final version4 doc 26 DEMETRA User Manual Calendar_1 Fixed day 5 December The data generated by each calendar can be viewed by a double click on the corresponding item in the workspace tree DEMETRA User Demetra User Manual final version4 doc 27 DEMETRA User Manual double click here click on the header to display the 11 19_ to display the default calendar 17 19_ periodogram f 1 1382 a 0 0 2 1982 0 0 0 0 25 31382 1 l i 4 1382 0 0 0 0 12 0 1 0 0 amp 1582 0 1 0 0 7 1982 0 0 1 0 81982 1 0 319382 0 0 0 bd r b k an am The regression variables can be inspected for any frequency monthly bi monthly quadri monthly quarterly half monthly yearly and any reasonable time span through that window The periodogram of those series is displayed when a column is selected Demetra presents three different v
138. n t t where s is the number of last available observations during penultimate execution of the multi processing n is the number of observations added to the revised time series k is the frequency of the time series for quarterly series k 4 for monthly time series k 12 Sid error T Stat ALT 2006 0 141 0 0108 AO 2 2006 0 2009 0106 0 0000 LS 5 2006 1009 0130 AO 6 2006 3588 0 01322 TC 8 2006 1506 0 013 11 23 AO 9 2006 0 1482 TCI6 2007 Ei Detected outliers Parameter Value Std error P value 19 2007 e ooz ROLTO 2007 To i0 2007 P AQ 6 2008 3997 0218 18 35 0 D000 LS 9 2008 TOC S 2008 LS 11 2008 DEMETRA User Demetra User Manual final version4 doc 179 DEMETRA User Manual Annex 1A Definition of the residuals Because of complexity X12 Arima and TramoSeats methods their implementation in Demetra is not exactly the same as in the software provided respectively by U S Census Bureau and Bank of Spain For this reason there are small differences between original programs and programs implemented in Demetra t It should be noted that the original solution of TramoSeats and the solution which was implemented in Demetra are exactly equivalent when the model doesn t contain regression variables The same is true for X12 only when the model is a pure AR model However in some specific cases short series many regression variables and or missing values residuals calculated by De
139. n aicdiff Demetra only considers pre tests on regression variables related to calendar effects trading days or moving holidays Trading days gt The user can choose between four ways of Type trading days estimation e None e Predefined e Calendar e UserDefined None means that Calendar effects will not be included in the regression Predefined means that default Calendar will be used Calendar option corresponds to the pre defined trading days variables modified to take into account specific holidays It means that after choosing this option the user should specify the type of trading days effect td1 td2 td6 or td7 and chose the calendar which will be used for holidays estimation UserDefined is used when the user wants to specify in a free way his own trading day variables With this option the calendar effect is captured only by regression variables chosen by user from the previously created User defined variables Trading days gt regression aictest Pretest the significance of the trading days rest LPR Megson verbs using states Trading days gt Acceptable values Details gt e Td include the six day of the week Trading days variables and a leap year effect DEMETRA User Demetra User Manual final version4 doc 51 DEMETRA User Manual Comments a e spec td1Coef include the weekday option is weekend contrast variable and a available if leap year effect Trading days tdNoL
140. n be re opened at a later point in time e Save as save the project file named by the user that can be re opened at a later point in time e View activates or deactivates the panels chosen by user Browsers Workspace Logs TS Properties e Edit allows defining countries calendar and regression variables this functionality is described further into this instruction e Import allows importing countries calendar and regression variables from Xml files this functionality is described further into this instruction e Recent Workspaces opens workspace recently saved by user e Exit closes an open project Workspace pen IS Save Save AS LOB View b Edit Calendars Import d User wariables Recent Workspaces P Exit DEMETRA User Demetra User Manual final version4 doc 24 DEMETRA User Manual 3 1 1 Calendars This functionality is helpful for detecting and estimating the trading day effects Trading day effects are those parts of the movements in the time series that are caused by different number of the weekdays in calendar months or quarters respectively As with seasonal effect it is desirable to estimate and remove trading day effects from the time series Trading day effects arise as the number of occurrences of each day of the week in month quarter differs from year to year The special case of the calendar effects is a leap year effect which cause regular variation because
141. n both sides of the Arima model This problem concerns mixed Arima P D Q BP BP BQ models i e p gt O and g gt Oor P gt O and Q gt O For example cancellation problem occurs with Arima 1 1 model 1 B z 1 6B a when as then model is simply form z a such model causes problems with convergence of the nonlinear estimation For this reason X12 and TramoSeats programs checks cancellation problem by computing zeros of the AR and MA polynomials As cancellation does not need to be exact the cancellation limit can be provided by the user 8A X12 tables Part A Preliminary Estimation of Extreme Values and Calendar Effects Table A1 Original series Table Ala Forecast of Original Series Table A2 Leap year effect Table A6 Trading Day effect 1 or 6 variables Table A7 Easter effect Table A8 Total Outlier Effect Table A8ao Additive outlier effect Table A8ls Level shift effect 94 Description based on X 12 ARIMA Reference Manual 2007 95 Description taken from X 12 ARIMA Reference Manual 2007 DEMETRA User Demetra User Manual final version4 doc 191 DEMETRA User Manual Table A8tc Transitory effect Part B Preliminary Estimation of Time Series Components Table B1 Original series Table B2 Unmodified Trend Cycle Table B3 Unmodified Seasonal Irregular Component Table B4 Replacement Values for Extreme S I Values Table B5 Seaso
142. nal Component Table B6 Seasonally Adjusted Series Table B7 Trend Cycle Table B8 Unmodified Seasonal Irregular Component Table B9 Replacement Values for Extreme S I Values Table B10 Seasonal Component Table B11 Seasonally Adjusted Series Table B13 Irregular Component Table B17 Preliminary Weights for the Irregular Table B20 Adjustment Values for Extreme Irregulars Part C Final Estimation of Extreme Values And Calendar Effects Table C1 Modified Raw Series Table C2 Trend Cycle Table C4 Modified S I Table C5 Seasonal Component Table C6 Seasonally Adjusted Series Table C7 Trend Cycle Table C9 S I Component Table C10 Seasonal Component DEMETRA User Demetra User Manual final version4 doc 192 DEMETRA User Manual Table C11 Seasonally Adjusted Series Table C13 Irregular Component Table C20 Adjustment Values for Extreme Irregulars Part D Final Estimation of the Different Components Table D1 Modified Raw Series Table D2 Trend Cycle Table D4 Modified S I Table D5 Seasonal Component Table D6 Seasonally Adjusted Series Table D7 Trend Cycle Table D8 Unmodified S I Component Table D9 Replacement Values for Extreme S I Values Table D10 Final Seasonal Factors Table D10A Forecast of Final Seasonal Factors Table D11 Final Seasonally Adjusted Series Table D11A Final Seasonally Adjusted Se
143. nal irregular component and final seasonal factors for each of the periods in a time series months or quarters To calculate them Demetra uses the active specification the one which is marked in the Workspace menu DEMETRA User Demetra User Manual final version4 doc 34 DEMETRA User Manual El Workspace_7 Eley Single processing AB Spectica 5 E xia x x x11 3 al 5 RSA A RSA2c l Jan Mar May Jul Sep Now _ AlZSpec 1 Feb Apr Jun Aug Oct Dec 2 Calendars R m Default The curves visible on the chart represent the final seasonal factors and the straight line represents the average for these values in each period For more detail see 4 3 2 1 1 6 WA Spectral analysis Demetra offers two spectral estimators periodogram and autoregressive spectral estimator After choosing one of them from Tools menu the empty window is displayed Tools L Container b TS Properties Options Chart Growth Chart Periodogram Seasonal chart Periodogram To calculate periodogram drag and drop a raw time series into the displayed window A methodological note about spectral analysis is available at the end of the Manual 7 For more information see the Annex section 7 DEMETRA User Demetra User Manual final version4 doc 35 DEMETRA User Manual E The auto regressive spectrum can be generated in the same way Ay
144. nderlying normality of the Arima model Three outliers types can be automatically detected e additive outlier AO which affects an isolated observation e level shifts LS which implies a step change in the mean level of the series e temporary transitory change TC which describes a temporary effect on the level of series after a certain point in timet 17 KAISER R and MARAVALL A 2000 DEMETRA User Demetra User Manual final version4 doc 62 DEMETRA User Manual ar Comments Individual spec Argument IsEnabled outlier Presence or not of the outlier individual spec Outliers outlier span Span used for the outlier detection The span detection span can be computed dynamically on the series for instance Excluding last 12 obs Use default outlier critical When Use default critical value is false the critical value procedure uses the critical value mentioned in the specification Otherwise the default is used the first case corresponds to critical xxx the second corresponds to a spec without the critical argument It should be noted that it is not possible to define separate critical value for each outlier s type Critical value outlier critical Critical value used in the outliers detection procedure AO outlier ao Automatic identification of additive outliers Automatic identification of level shifts Automatic identification of transitory changes TC rate outlier tc
145. next two figures 70 MARAVALL A 2003 71 PLANAS C 1998 72 Squared gain definition is given in the Annex section 5A 73 PLANAS C 1998 DEMETRA User Demetra User Manual final version4 doc 146 DEMETRA User Manual squared gains derived from two different models are represented In the first graph the squared gain of the seasonal adjustment filter shows large throughs to suppress very erratic seasonal component while in the second graph it shows more narrow throughs to remove a more stable seasonality Sth 4 0 8 z 0 6 0 4 0 2 0 e WK filter Wiener Kolmogorow filter V b F shows the weights that have been applied to the original series x to extract the i th component xi in the following way see the Annex section 5A for description of the WK filter A X it V B F x DEMETRA User Demetra User Manual final version4 doc 147 DEMETRA User Manual where V B F v v B F j l Since WK filters are symmetric and centered It is also convergent which enable to approximate infinite number of realization x by finite number of them from the graph below it could be noticed that j 36 In order to apply filter to all observations of the x original time series is extended with forecasts and backcasts using ARIMA model As new observation i e observation for period t 1 is available forecast for period t 1 is replaced by this new observation and all f
146. nition and Hannan Quinn Those criteria are used in seasonal adjustment procedures for the selection of the proper Arima model The model with the smaller value of the model selection criteria is preferred The charts below present an exemplary output Data transformation Estimation span 1 2000 1 2010 Model ation Number of effective observations 106 Number of estimated parameters 11 Loglikelihood 329 7818 Standard error of the regression ML estimate 5 07962 AIC 681 5635 AICC 684 3135 BIC 711 0670 BIC Tramo definition 3 6840 Hannan Quinn 693 5261 Next the estimated model parameters their standard errors t statistics and corresponding p values are displayed Demetra uses the following notation d regular difference order D Seasonal difference order Phi p regular AR parameter in p order Th q regular MA parameter in q order BPhi P seasonal AR parameter in P order BTh Q seasonal MA parameter in Q order In the example below the Arima model 0 1 0 0 1 1 was chosen which means that only one seasonal moving average parameter was calculated The p value indicates that the regressor is significant 29 Maximum Likelihood Estimation is a parameter estimation method that determines the parameters that maximize the probability likelihood of the sample data 30 AIC AICC BIC and Hannan Quinn criteria are used by X12 while BIC Tramo definition by TramoSeats Informati
147. nt software namely Demetrat which covers the recommendation of ESS guidelines in this area Demetra has been developed by the National Bank of Belgium The application seasonally adjusts large scale sets of time series and provides user friendly tools for checking the quality of the SA results Demetra includes two seasonal adjustment methods X 12 Arima and TramoSeats As Demetra IT solutions are utterly different from the old Demetra all files created in Demetra are not read by Demetra Demetra is no more developed nor supported by Eurostat The manual aims to introduce the user to the main features of the Demetra software and to make the user able to take advantage of the powerful tools provided This document presents an overview of the software capabilities and of its main functionalities Moreover step by step descriptions how to solve some basic tasks are included The User Manual will give the possibilities for reproducing results with user s own data The guide shows the typical paths to follow and illustrates the user friendliness of Demetra The reader is expected to have already acquired background knowledge about the concept of seasonal adjustment and is familiar with X 12 Arima and TramoSeats methods For those readers interested in studying the seasonal adjustment methods in detail bibliography is provided at the end of the manual It should be emphasized that Demetra makes use of X 12 Arima and TramoSeats algorithms restr
148. nual e Components H Main results H Fre processing Tramo Decomposition Seats Stochastic senes Model based tests WK analysis EEE One e Preliminary estimators Emors analysis ce Diagnostics This section presents the pseudo spectra of the particular components The sum of the components spectra should be equal to the spectrum for the observed time series which is presented in the Pre processing Tramo part if the Tramo model has been accepted by Seats the figure displays one spectra otherwise spectra of the model chosen by Seats is visible A seasonally adjusted series spectra dark blue is sum of trend cycle component spectra red transitory component spectra green if present and irregular component spectra pink Since a generates the stochastic variability in the i th component small values of V a are associated with stable component large values of V a with unstable component The spectrum of the i th component is proportional toV a It means that stable trend and seasonal component are those with thin spectral peaks while unstable ones are characterised by l HAAS wide spectral peaks For monthly time series there are six seasonal frequencies 77 63 2 6 0 T while for quarterly data there are two seasonal frequencies r Spectrum for seasonal component peaks around these frequencies On the figure below the trend cycle spectrum red is relatively narrow w
149. nual oO 05 Oo Oo Oo Oo ol oO m o 0 go to AB Ee og 0 5 e Errors analysis H Main results fe Pre processing Tramo Decomposition Seats e Stochastic series z Model based tests Ey WE analysis z Final estimators E Diagnostics An error analysis is performed in last WK analysis node Formulas for estimation errors are included in the Annex section 5A o Total estimation errors This panel reports the variance of the total estimation error of the trend cycle seasonally adjusted series seasonal and irregular for concurrent estimators lag 0 and for preliminary estimators lag lt 0 These variances are reported in units of the variance V a The X axis shows the duration of the revision process i e how many periods it takes for a new observation to no longer significantly affect the estimate DEMETRA User Demetra User Manual final version4 doc 154 DEMETRA User Manual 0 6 5 0 5 eo9 9 080 7 0 4 oe 0 ee 9 59 6 Oo ee T gt 8 6 E O O 8 O E ests egtriibs p o 9 bogo a e B 3 l e 5 co e a D G g o e F 4 fa o m 35 30 25 20 15 10 5 0 o Revision error Revision error is the difference between preliminary and final estimator For each component the graph shows the percentage reduction in the standard error of the revision after additional periods up to 3 years Comparisons are made with concurr
150. o the current workspace 2 by preliminary choice of the seasonal adjustment method Single seasonal adjustment processing can be defined by choosing TramoSeats specification or X12 specification from main menu Seasonal adjustment Crear ifr atnm ee TEER apecmcatons Tramo Seats specification single analysis X12 specifications Multi processing Then the new specification window will be displayed with default settings The user is allowed to change them After clicking OK button the new specification is added to the specifications list in Workspace TramoSeats or X12 specifications list depending on initial choice DEMETRA User Demetra User Manual final version4 doc 84 DEMETRA User Manual TramoSeatsSpecDig l E adl Workspace d RSA0 Calendar effects Selection type All RSA 4 Anma modeling Fc RSAZ Outliers detection RSA Estimation RSAA Decomposition Seats Tram Seats Spec 1 Tramo Seats Spec 2 Tramo Seate Spec 3 None no transformation Log tanes of date mr ieman ao alra ponia ed omy ASAA 3 by cloning specification The new specification can be created directly in the Workspace window by clicking on the existing specification pre defined or previously created by the user and choosing option Clone New specification will be added to the specifications list The pictures below illustrate this solution First the option Clone has been chosen for X12 Spec 4 2i
151. od Fabrication d autres produi 12 RS Concurrent Valid 6 Good Fabrication de boissons 0 X12 R5 Concurent Valid 6 Good basic checks Fabrication de produits b 12 R5 Concurrent Valid 10 Good definition Good 0 000 Fabrication de produits de 12 R5 Concurrent Valid T annual totals Uncertain Fabrication de produits laiti 12 R5 Concurrent Valid 6 0 021 Fabrication dhuiles et grai 12 R5 Concurrent Valid T Industries alimentaires 001 X12 R5 Concument Walid 6 Transformation et conser X12 A5 Concurrent Valid 6 Transtommation et conse X12 A5 Concurrent Valid 6 Travail des grains fabrica 12 R5 Concurent Valid 6 spectral td peaks Good reganima residuals normality Bad 0 009 independence Good 0 265 S spectraltd peaks Good 7 Fabrication de produits a base de tabac 001563044 5A series PATIT ee Sayre FAD A ea i a N i y ry 01 1990 01 1992 07 1994 01 1996 07 1996 01 2000 01 2002 01 2004 01 2006 01 2008 01 2010 For particular time series the user can modify priority value manually by clicking on the time series name in SAProcessing window and choosing Priority value from the list from 1 to 10 EF SAProcessing 6 4 z Ol x Series Method Processing Priority Quality Warning Fabrication d aliments pour X12 R5 Concurrent Valid 6 Good Fabrication d autres produi X12 R5 Concurent Valid 6 Good Fabrica
152. odel in terms of revisions More detailed description is available in the Annex section 10A 112 110 108 106 104 2 100 i a H oY E N i 98 96 06 2005 11 2005 04 2006 09 2006 02 2007 07 2007 12 2007 05 2008 10 2008 03 2009 08 2009 If the user clicks on a blue circle which represents the initial estimation for period ft an auxiliary window will appear The figure shows the successive estimations computed on f tost l fo t7 of the considered series for the period t From this figure the user can DEMETRA User Demetra User Manual final version4 doc 115 DEMETRA User Manual evaluate how the seasonally adjusted observations have been changing from initial to final estimation The analogous graph is available for trend analysis 112 110 108 102 100 A o o TF N Pi h ft i i i i 7 2 6 g i y Y g 06 g4 06 2005 11 2005 04 2006 109 08 2009 04 2006 02 2007 42 2007 10 2008 08 2009 09 2006 07 2007 05 2008 03 2009 01 2010 The user could establish the size of the revision using the vertical axis In the figure above the revisions are about 5 The figure size could be enlarged by dragging the bottom right corner By default only the parameters of the model are re estimated It is also possible to make a complete re estimation or a re identification of the outliers That option can be changed through the local menu of the revision history node left panel at t
153. oefficients of every outlier are specified in node Pre processing RegArima Second part of Main Results aims to inform the user about quality of the seasonal adjustment by reporting a summary of diagnostics Summary Basic Checks Visual spectral analysis regarima residuals residual seasonality outliers m statistics parts are described further summary Severe basic checks definition Good 0 000 annual totals Good 0 001 visual spectral analysis spectral seas peaks Good spectral td peaks Good regarima residuals normality Good 0 910 independence Uncertain 0 071 spectral td peaks Severe 0 000 spectral seas peaks Uncertain 0 011 residual seasonality on sa Good 0 418 on sa last 3 years Good 0 350 on irregular Sood 0 21 outliers number of outliers Good 0 022 m statistics q Good 0 564 q without m2 Good 0 509 In the Charts section the top panel presents the original series with forecasts the final seasonally adjusted series the final trend with forecasts and the final seasonal component with forecasts The second panel shows the final irregular component and the final seasonal component with forecasts DEMETRA User Demetra User Manual final version4 doc 90 50000 40000 30000 20000 10000 4 Vy A Je P J A Jes A PA Nepal 0 01 1991 01 1993 01 1995 01 1997 01 1999 01 2001 01 2003 01 2005 01 1992 01 1994 01 1996 01 1998 01 2000 01 2002 01 2004 DEMETRA User Manual
154. of m when the last observation is x x is a time series d can be presented as the sum of the final estimation error e and the revision error 7 A A A A Best MN Mitlt k X a Xit a Xi Xitlt k a ray The final estimation error e and the revision error r are assumed orthogonal 93 MARAVALL A 2000 DEMETRA User Demetra User Manual final version4 doc 190 DEMETRA User Manual 6A Initial values for Arima model estimation The default choice of initial parameter values in X12 is 0 1 for all AR and MA parameters For majority of time series this default value seems to be appropriate Introducing better initial values as might be obtained e g by first fitting the model using conditional likelihood could slightly speed up convergence Users are allowed to introduce manually initial values for AR and MA parameters that are then used to start the iterative likelihood maximization This is rarely necessary and in general not recommended A possible exception to this occurs if initial estimates that are likely to be extremely accurate are already available such as when one is re estimating a model with a small amount of new data added to a time series However the main reason for specifying initial parameter values is to deal with convergence problems that may arise in difficult estimation situations 7A Cancellation of AR and MA factors A cancellation problem consists in cancelling some factors o
155. of the extra day inserted into February every four years These differences cause regular effects in some series Both X12 and TramoSeats estimate trading day effects by adding regressors to the equation estimated in the pre processing part RegArima or Tramo respectively Regressors mentioned above are generated on calendar basis The calendars of Demetra simply correspond to the usual trading days contrasts variables based on the Gregorian calendar modified to take into account some specific holidays Those holidays are handled as Sundays and the variables are properly adjusted to take into account long term mean effects Demetra considers three kinds of calendars e National calendars identified by specific days e Composite calendars defined as weighted sum of several national calendars e Chained calendars defined by two national calendars and a break date The calendars can be defined recursively It is also possible to define calendar using User defined regressors The dialog box allows defining all calendars described above In the column on the right the number of calendars already defined is shown 6 The user can also use default calendar to define composite calendar and chained calendar DEMETRA User Demetra User Manual final version4 doc 25 DEMETRA User Manual a PropertiesDig If the user chooses the option National calendars the following window is displayed The user can define new calendar Add button or
156. oint normality assumption Xinr is also equal to the conditional expectation E s X so it can be presented as a linear function of the elements in X A Xir HV X p HHX 04 V X tk Fee when T the estimator becomes final historical estimator In practice it is achieved for large A k When T k lt t lt T xar yields a preliminary estimator and for t gt T a forecast The join distribution of the stationary transformation of the components and of their MMSE estimators i e variances autocorrelations and cross correlations is used for model diagnostic A For each component the estimate xiir is obtained by applying Wiener Kolmogorow V B F filter on x X it V B F x where 84 HARVEY A C and KOOPMAN S J 1992 85 Term spectrum is used for stationary time series while term pseudo spectrum is used for non stationary time series for no stationary time series spectrum is not defined In majority of cases components extracted from original time series are non stationary Pseudo spectrum is defied as 2 6 7 2 1 cos 2w ae MARAVALL A and PIERCE D A 1986 e Sx DEMETRA User Demetra User Manual final version4 doc 185 DEMETRA User Manual L V B F 0 gt 0 B F j l which is symmetric In practice L typically expands between 3 and 5 years Hence when T gt 2L 1 where T is the last observed period final estimators can be a
157. om the Tools menu see Chapter 3 2 DEMETRA User Demetra User Manual final version4 doc 113 DEMETRA User Manual Two spectrum estimators are implemented periodogram and auto regressive spectrum Seasonal frequencies are marked as grey vertical lines while violet lines correspond to trading days frequencies The X axis shows the different frequencies The periodicity of phenomenon at 27 frequency f is It means that for monthly time series the seasonal frequencies are A series the frequency 3 corresponds to a periodicity of 6 months 2 cycles per year are T completed For the quarterly series there are two seasonal frequencies z one cycle per year and z two cycles per year Peak at the zero frequency always corresponds to the trend component of the series For more detail about spectral analysis refer to the Annex section 9A 40 Periodogram A 0 Pli2 FI Auto regressive spectrum 0 Pli2 FI At seasonal and trading days frequencies a peak in the residuals indicates the need for a better fitting model In particular peaks at the seasonal frequencies are caused by inadequate filters chosen for decomposition Peaks at the trading days frequencies could occur due to inappropriate regression variables used in the model or the significant change of the calendar effect because the calendar effect cannot be modeled by fixed regression effect on the whole time series span A peak in the spectrum of
158. om the second in this manner and a fourth from the third data permitting This is done in such a way that the last span contains the most recent data DEMETRA User Demetra User Manual final version4 doc 119 DEMETRA User Manual The summary of the sliding spans analysis is presented below It contains information about spans results of the seasonality tests for each span and means of seasonal factors for each month in each span For seasonality tests descriptions see the Annex section 12A Time spans Span 1 from 1 1998 to 11 2006 Span 2 from 1 1999 to 11 2007 Span 3 from 1 2000 to 11 2008 Span 4 from 1 2001 to 11 2009 Tests for seasonality Stable Seas Kruskal Wallis Moving seas dentable sees Means of seasonal factors Span 3 Span 4 January 11212 August September 1103 8532 78 The seasonal and the trading day s panels compare the relative changes of the levels of those components The SA changes panel is related to period to period percent changes When an additive decomposition is used the sliding spans analysis uses absolute differences The threshold to detect abnormal values is set to 3 of the testing statistics see the Annex section 11A Detailed results of the sliding spans analysis is conducted separately for seasonal component trading days effect and SA series changes The description of these results is the same for each part of the series Below explanation of the outpu
159. omatic modelling nescssesereresusrererreresurrerereresueserererrurrersreresens 74 42o Anma Modea E 75 ADJ Outliers detecto saana a E E TNN 76 M280 ESMA UO Nea E S a a 77 4 2 9 DECOMPOSITION SCAUS arr a A T a A 78 4 3 SINB IE OPOCESSING aenn a e A E E 79 43 1 B fmMing asingle ProcessiNg esne a a a N TO 79 4 3 1 1 Creation of a single processing using existing specification sessssessrersesreresrrrseree 79 4 3 1 2 Creation of a single processing by defining new SPECIFICATIONS c cceeeeeceeeeeeeees 82 DEMETRA User Demetra User Manual final version4 doc 4 DEMETRA User Manual 4 3 2 Seasonal adjustment results single processing ccccccccssecccceeesececeeseceeeeeeceeeeeeeeeas 86 Seed E E E eis ol nia ee ateeuces tan 88 432 kht MIANAOSUILS erena pesbendemeaaeeics pak tuveangcnndonsusienadtaanes bu guteeauumieelamaanrdees 89 D212 PrO POCES SINE err sevwuieupurncseapondauasounceectanseeceiind ES 94 43 2 13 DECOMPOSIEION sates ductal e n E T 101 W352 kA DIENOS STC S enee a A AA 104 A32 2a aM ea Saa E E E EE 126 4322 e Man FOS UIGS aisa A N 127 4 3222 Preprocessing IAIN 0 aoine r A AS 130 43 2 23 DECOIMPOSIEIOMN descise nui E T E E E 135 A 22A DIASMOSUICS oaea AE E a 156 AAs Muk processiNE iss a a EA 157 AAi Denning a Multi processiNe seiprssiae 157 4 4 2 Seasonal adjustment results for MUItI PrOCESSING cccccccsssecceceesececeeeceeseeseeeeenecss 160 AAD A Generalii Se
160. on OOOO Esmor Estimate Pave rendiseasonal Joasi 0 2073 0 5748 trend transitory 0 4470 0 3754 0 4813 It is expected that the theoretical cross correlations between the component estimators will be close to their sample estimates 64 GOMEZ V and MARAVALL A 2001 65 GOMEZ V and MARAVALL A 2001 66 GOMEZ V and MARAVALL A 2001 67 MARAVALL A and CANETE D 2011 DEMETRA User Demetra User Manual final version4 doc 141 DEMETRA User Manual Wiener Kolmogorow analysis H Main results H Pre processing Tramo Decomposition Seats 2 Stochastic seres Wiener Kolmogorow analysis concerns results obtained by Seats and concentrates on 8 e Components spectrum ACGF e Final estimators spectrum square gain function WK filters ACFG PsiE weights e Preliminary estimators Frequency response square gain function phase effect WK filter ACFG e Revision analysis total error revision error This section presents various graphs concerning components of time series As a rule dark blue color indicates seasonally adjusted time series navy blue indicates seasonal component red indicates trend cycle green indicates transitory and pink indicates irregular component 68 Wiener Kolmogorow analysis is described in e g MARAVALL A 1993 MARAVALL A 2008 MARAVALL A 2006 MARAVALL A 1995 DEMETRA User Demetra User Manual final version4 doc 142 DEMETRA User Ma
161. on criteria formulas are given in the Annex DEMETRA User Demetra User Manual final version4 doc 95 DEMETRA User Manual ARIMA model 0 1 0 0 1 1 Parameter Value Sid enor T 5tat P value BTh 1 0 3376 00882 0 0002 For fixed Arima parameters see 4 1 3 4 Demetra shows only the parameters values From the example below it is clear that the user has chosen manually Arima model 0 1 1 0 1 1 with fixed parameter Th 1 ARIMA model 0 1 1 0 1 1 Parameter value Std error Thi 0 7220 as BTh 1 0 8613 0 0489 17 62 If Arima model contains a constant term detected automatically or introduced by the user estimated value and related statistics are reported Mean effect Parameter Value Std eror F yalue 0 0007 0 0001 0 0000 Demetra presents estimated values of coefficients of one or six regressors depending on the calendar effect specification s type Joint F test value is reported under the estimated values if six regressors specification are chosen If a leap year regressor has been used in the model specification estimated leap year coefficient value is also reported with its standard error t statistics and the corresponding p value If option UserDefined in calendar effect has been chosen Demetra displays User defined trading days section with variables and theirs estimation results parameters values standard errors t statistics and corresponding p values and joint F test result In
162. on et conser X12 R5 Concument Valid Transformation et conserv 12 RS Concurrent Valid Fabrication dhuiles et grai X12 R5 Concurrent Valid Fabrication de produits laiti X12 R5 Concurrent Valid Travail des grains fabrica 12 R5 Concurrent Valid Fabrication de produits de X12 R5 Concurrent Valid Fabrication d autres produi X12 RA5 Concurrent Valid Fabrication d aliments pour X12 RS Concument Valid Fabrication de boissons 0 X12 R5 Concurrent Valid Fabrication de produits ab 172 R5 Concurrent Valid basic checks definition Good 0 000 annual totals Uncertain 0 266 0 gt spectral td peaks Good gt Fabrication de produits a4 base de tabac 001563044 ren SA series FOs Mt LAL F Api Aa Aki i i T iit kid 200 vy NAA Duh r 0 01 1990 01 1992 01 1994 01 1996 01 1998 01 2000 01 2002 01 2004 01 2006 01 2008 01 2010 New processing 11 items The user can calculate it automatically by choosing one of the Priority options available in SAProcessing menu m j LI Add to workspace Initial order Priorities will be added to the SAProcessing output window DEMETRA User Demetra User Manual final version4 doc 174 DEMETRA User Manual Ee SAProcessing 6 Processing Summary Matrix view Se eries Estimation Processing Priority Quality Warning summary Fabrication d aliments pour X12 RS Concument Valid 6 Good Go
163. ool The closeness between estimators and estimates points towards validation of the results e Cross correlation function The decomposition made by Seats assumes orthogonal components To test this assumption Demetra calculates cross correlations among the stationary transformations of both the estimators and actual estimates theoretical components are uncorrelated A table containing these correlations is presented they refer to trend and seasonal trend and irregular seasonal and irregular and if the transitory is present trend and transitory seasonal and transitory irregular and transitory Although components of the time series are assumed to be uncorrelated their estimators can be correlated as estimator variance will always underestimate the component variance The appearance of the cross correlation between the estimators of components has been signaled as an inconvenience of the model based approach For this reason correlations between the Stationary transformations of the estimators and of the estimates actually obtained should be checked The last column PValue in the table below displays the results of the test for no correlations between components The outcome of the test is signalized by the color of the p value see table above In the example below PValues are green which indicates that all correlations are negligible so for each component estimator and estimate provide similar results Cross correlati
164. or Estimation of the Noise in Unobserved Component Models Journal of Business amp Economic Statistics American Statistical Association vol 5 1 115 20 MARAVALL A 1993 Stochastic linear trends Journal of Econometrics 56 1993 5 37 DEMETRA User Demetra User Manual final version4 doc 208 DEMETRA User Manual MARAVALL A 1995 Unobserved Components in Economic Time Series in H Pesaran and M Wickens eds The Handbook of Applied Econometrics Oxford MARAVALL A 2000 An Application of Tramo and Seats in Annali di Statistica Seasonal Adjustment Procedures Experiences and Perspectives 129 X 20 MARAVALL A 2006 An application of the TRAMO SEATS automatic procedure direct versus indirect adjustment Computational Statistics amp Data Analysis 50 2006 2167 2190 MARAVALL A 2003 A class of diagnostics in the ARIMA model based decomposition of a time series in Seasonal Adjustment European Central Bank MARAVALL A 2008 Notes on Programs TRAMO and SEATS TRAMO part http www bde es webbde es secciones servicio software tramo Part Il Tramo pdf MARAVALL A 2008 Notes on Programs TRAMO and SEATS SEATS part http www bde es webbde es secciones servicio software tramo Part Ill Seats pdf MARAVALL A and CANETE D 2011 Applying and interpreting model based seasonal adjustment The Euro Area Industrial Production Series Documentos
165. or the trading days Details gt iuser ilong the type UserDefined the corresponding Items nser variables should be specified It should be noted that such variables should have been option S previously defined see 3 1 2 available if Trading days UserDefined Easter Others The option enables the user to treat the IsEnabled TradingDay Easter Easter effect in three different ways Effect The user can choose between e No e Pretest e Yes No a correction for Easter effect is not performed Pretest Demetra estimates the Easter effect if statistical tests shows that this effect is significant Yes the correction for Easter effects is performed For last two option the user can modify the default length of the Easter effect default length is 6 days Duration Others idur Duration of the Easter effect w parameter TradingDay Easter of the easter variable The parameter is Effect active if the iest Pretest or Yes The current version of Demetra doesn t allow the use of stock trading days Pre defined calendar day for the handling of Labor Day and of Thanksgiving are not available see 3 1 1 for list of pre defined holidays Nevertheless the user is allowed to create any fix day regression variable DEMETRA User Demetra User Manual final version4 doc 69 DEMETRA User Manual Example predefined trading days Example calendar trading days Holidays z Duration
166. orecasts for periods g gt t 1 are updated It means that near the end of time series estimator of the component is preliminary and is a subject of revisions while in the central periods estimator will be treated as final also called historical Since WK filters are symmetric and convergent they are valid for computing the estimators in the central periods of the sample The following graph demonstrates these features The following graph demonstrates weights that are applied to the each observation for each component weights applied to seasonally adjusted series are dark blue to trend cycle are red to transitory component are green and to irregular component are pink 5 fa a Oooo ood TET Per oCoogagg o 0 eeccooeees gevasagass SeoonoooT FoHsoosos g8R8GR8SER EReoeeoooes ELET T TE 3g oogoco oR jg A o 74 MARAVALL A 2011 DEMETRA User Demetra User Manual final version4 doc 148 DEMETRA User Manual o Auto Correlation Generating Function The window ACGF stationary displays the auto correlation functions of the final estimators of the stationary components The following graph represents an example 3 0 5 H o o H o ao o ona O g oO oo o Bogga Bog Oo 0 o H Bo o EBBEO gog B B o A B e B B E o o z o m m O g H o f o 0 5 0 a Oo 4 o PsiE weights PsiE weights y are a different representation of the final estimator as they are applied to the
167. out seasonal adjustment and the quality of the outcomes are divided into three parts Pre processing Tramo Decomposition and Diagnostics E Main results Chai Taie L Sd ratio H Pre processing Tramo H Decomposition Seats ce Diagnostics First part contains results from Tramo Information Series has been log transformed is displayed if logarithmic transformation has been applied as a result of specification test done by Tramo Otherwise information does not appear In case of RSAO RSA1 and RSA3 specifications trading days effect is not estimated For RSA2 and RSA4 specifications working days effect and leap year effect are pretested and estimated If working day effect is significant pre processing part includes information Working days effect 1 regressor Working days effect 2 regressors means that also leap year effect is significant For RSA5 specification trading days effect and leap year effect are pretested If the trading days effect has been detected Trading days effect 6 regressors or Trading days effect 7 regressors is displayed depending whether leap year effect has been estimated or not If Easter effect is statistically significant in the series Easter effect detected is displayed If RSAO specification is used or any significant outliers have not been found under other specifications No outliers found is displayed In this section only total number of detected outliers is visible More info
168. pYear include the six day of Predefined the week variables or Calendar td1NoLpYear include the weekday type weekend contrast variable Some options can be disabled when the adjust option is used in the transformation specification Trading days gt regression variables Acceptable values Details gt e LeapYear include a contrast Length of period variable for leap year LengthofPeriod include length of option is month or length of quarter as a available if regression variable Trading days Can be disabled when the adjust option is Predefined used in the transformation specification or or Calendar with some trading days options type Trading days gt When the user chooses the calendar type Details gt for the trading days one must specify the Holidays corresponding holidays It should be noted that such a holiday must have been option is previously defined see 3 1 1 available if Trading days Calendar type Trading days gt regression user When the user chooses the userdefined Details gt usertype type for the trading days one must specify Items td the corresponding variables It should be noted that such variables must have been option is previously defined see 3 1 2 available if Trading days UserDefined Easter gt regression variables The option enables the user to estimate the IsEnabled and or Easter effect in three different ways aictest The user can choo
169. pectral peaks at seasonal frequencies and the irregular component captures white noise behavior Transitory component contains short term variability associated with low order MA components of order Q P when Q gt P and AR roots with small moduli that should not be included in the trend cycle or seasonal component Moreover transitory component captures periodic fluctuation with period longer that a year associated with a spectral peak for a frequency between 27 O and where s is a number of observations per year and periodic fluctuation with s spectral peak for intraseasonal frequencies 54 It is assumed that irregular component is a white noise variable which means that it follows ARIMA 0 0 0 0 0 0 model 55 MARAVALL A 1995 DEMETRA User Demetra User Manual final version4 doc 135 DEMETRA User Manual The example of time series decomposition calculated by Seats is presented below It can be seen that overall autoregressive polynomial has been factorized into polynomials assigned to the components according to the roots frequencies As an example the model for trend is 1 2B B4 D Xiong 0 059791B 0 94021B a highest variance 0 1454 and follows ARIMA 0 0 0 0 0 0 model 1 1 A mnovatoni 1 U nowationd rendt The innovation has the Decomposition Model Non stationary AR 1 B B 12 B 13 Stationary AR 1 0 386007 B 0 3327 B 2 MA 1 047638 B 12 Innovation var
170. pectral td peaks Good normality Good 0 234 independence Good 0 262 Unemployment SA series 1000 01 1995 01 1997 01 1999 01 2001 01 2003 01 2005 01 2007 01 2009 01 2011 01 1996 01 1998 01 2000 01 2002 01 2004 01 2006 01 2008 01 2010 New processing 7items 1 1 0 0 1 1 ao 2 tc 1 Is 2 The Summary panel gives general information on the results obtained from each method for each frequency monthly and quarterly The example below shows that TramoSeats method has been chosen for four time series Three of them have been logarithmically transformed The list of the Arima models shows the model parameters used in time series set There were 28 outliers detected the majority of which were additive outliers Calendar effects weren t detected for any of the time series seasonally adjusted using TramoSeats method DEMETRA User Demetra User Manual final version4 doc 161 DEMETRA User Manual lox E Reports Tramo Seats number of series 4 Tramo Seats Transformation Log transformations 3 75 00 Arima models 3 1 0 0 1 1 1 25 00 1 1 0 0 1 1 1 25 00 0 1 0 0 1 1 1 25 00 0 1 0 1 0 1 1 25 00 Mean correction 1 25 00 Outliers All outliers 26 average 7 00 Additive outliers 12 average 3 00 Level shifts 6 average 1 50 Transitory changes 10 average 2 50 Calendar effects Trading days corrections 0 0 00 5 Leap year corrections 0 0 00 5a
171. r RSA5 Tramo Seats Spec 1 Tramo Seats Spec 2 B E X12 X11 currently active specification RSA1 RSA3 RSA4c RSA5c X12Spec 1 El Calendars Default A User defined variables Right click on any existing name opens the pop up menu which contains the following commands Open Exclude Delete Clone Active Open opens the specification window with information on parameters The user can t change them The same result is achieved by double click on the specification s name Exclude remove the specification marked It works only for specifications defined by the user Delete remove the specification marked It works only for specifications defined by the user Clone creates new specification identical with the marked one The parameters of the newly created specification can be edited by the user Active activates the chosen specification Time series will be seasonally adjusted using this specification E Workspace_1 El e Single processing Tramo Seats gt X12 Multiprocessing Specifications asa TramoSeats RS Open RS RS Delete RS Clone Active RSA1 RSA2c RSA3 mernvaae In a similar way the user can add a new specification in single processing and multi processing sections This can be achieved by right clicking on the seasonal adjustment method DEMETRA User Demetra User Manual final version4 doc 20 DEMETRA User Manual
172. ra WorkspaceControl null 4 WorkspaceControl initialized z When the multi processing was created the user should add it to the workspace and then saved it using the options from multi processing menu Then one can use this multi processing for regular data production month to month or quarter to quarter This process should be conducted in the following way 1 Update the time series in the external file or source from which the variables come from e g update the file data xls with the new observations but don t change neither the file s name nor its location Start Demetrat Chose the multi processing from the workspace tree by double clicking on it gt TramoSeats BS x12 oof X12Doc 1 4 Choose in which way you would like to refresh the results7 78 For more details see 5 2 DEMETRA User Demetra User Manual final version4 doc 169 DEMETRA User Manual SAProcessing 1 Run Current adjustment partial Bettialconcurent adjustment gt parameters Concurrent adjustment Last outliers params All outliers params Arima and outliers params Initial order 5 Confirm that you want to refresh the data Demetra Are you sure you want to refresh the data o Aru 6 Choose the option Generate output form the menu Update reports Refresh Edit Priority A rii ELIN Initial ord
173. raphics are presented showing properties of preliminary estimators estimated by WK filter of each theoretical component Preliminary estimators are obtained by replacing observations not yet available with forecasts and extending series with backcasts Both forecasts and backcasts are obtained from Arima model Then filter is applied to the extended series There lag is set by default to zero so the semi infinite concurrent estimators xin are considered User can set a different lag from 1 up to 60 and therefore consider semi infinite preliminary estimators Xim j 76 See the Annex section 5A DEMETRA User Demetra User Manual final version4 doc 150 DEMETRA User Manual In this part different types of graphics which show properties of preliminary estimators estimated by WK filter of each theoretical components are presented The graphs include e Frequency response window contains two graphics i e the squared gain function and the phase effect Squared gain of preliminary estimators filter determines which frequencies will contribute to the component that is it filters the spectrum of the series by frequencies see aforementioned description of the sugared gain The phase effect graphics shows the phase shift in the seasonally adjusted series or trend cycle in comparison with original series It means that the phase effect indicates how frequency components are shifted in time by the filter so it measures the d
174. rate Rate of decay for transitory change outlier regressor Method outlier method Determines how the program successively adds detected outliers to the model could be add one by one the outliers with the highest insignificant t statistic are added removed at one time and the Arima model estimated and so on or add all outliers together all the significant insignificant outliers are added removed at once and the Arima model estimated and so on LS Run outlier Isrun Compute t statistic to test null hypotheses that each run of n Isrun successive level shifts cancels to form a temporary level shift ke defaul cilical value ries usi Lol Voc DEMETRA User Demetra User Manual final version4 doc 63 DEMETRA User Manual 4 1 9 Estimation Individual spec Comments Precision used in the optimization procedure 2 Transformation a Calendar effects _ Regression fH Arima modelling Outliers detection Precision 4 1 10 X12Spec 1 Precision 1E 05 ftol Precision used in the optimization procedure Decomposition X11 Individual Argument Comments spec a DEMETRA User Demetra User Manual final version4 doc Only multiplicative additive or logAdditve mode is possible Pseudo additive mode is not supported If the transformation is set to Log mode can be set into Multiplicative or LogAdditve If the transformation is set to None Mode is automatically se
175. rce Xml Excel TSW USCB l All series Monetary Aggregate ALP Spain CPI Spain EXPORTS JAPAN GNP USA IMPORTS DEMETRA User Demetra User Manual final version4 doc 18 DEMETRA User Manual 2 3 TS Properties The TS Properties window an abbreviation from Time Series Properties can be used for examining the characteristics of individual raw series This panel is strictly connected with Browsers The window is presented at the bottom part of the picture below TS Properties window presents the basics statistics chart and time series data The function is launched by single clicking on the time series name in Browsers window TS Properties provides also information about the name and source of the time series displayed in it TS Properties Name Unemployment Source XCLPRVDR jan 1995 2875 1 1996 2718 1 1997 2336 3 1998 1893 3 Metadata Statistics Time span 1 1995to 11 2010 Number of observations 191 Number of missing values 0 Min 1352 3 1999 2046 8 Max 3344 2 2000 2476 1 Average 2411 411 2001 2835 6 Median 2445 4 2002 3253 3 2003 3320 6 2004 3293 2 2005 3094 9 2006 2866 7 2007 2365 8 2008 1813 4 2009 1634 4 Stdev 549 38988543128 1000 01 1995 01 1997 01 1999 01 2001 01 2003 01 2005 01 2007 01 2009 01 2011 01 1996 01 1998 01 2000 01 2002 01 2004 01 2006 01 2008 01 2010 2 4 Workspace feb 2832 2 2734 2312 5 1891 9 214
176. relative contribution of stable and moving seasonality 3 Statistics M8 to M11 measure if the movement due to short term quasi random variations and movement due to long term changes are not changing too much over the years If the changes are too strong then the seasonal factors could be erroneous Q statistic is a composite indicator calculated from M statistics eA A a eee a 100 Q without M2 also called Q2 is the Q statistic without the M2 statistics If time series does not cover at least 6 years statistics M8 M9 M10 and M11 cannot be calculated In this case the Q Statistics is computed as eee E E E E A cc 100 The model has a satisfactory quality if Q statistic is less than 1 Results of the test Treshold 1 21 32 For the definitions of the M statistics see LADIRAY D and QUENNEVILLE B 1999 33 See the Annex section 12A DEMETRA User Demetra User Manual final version4 doc 103 DEMETRA User Manual Monitoring and Quality Assessment Statistics 0 801 4 3 2 1 4 Diagnostics The Diagnostic panel contains detailed information on the seasonal adjustment process H Main results H Pre processing RegArma E Decomposition X11 BT oases Seasonality tests H Spectral analysis H Revisions history H Sliding spans H Model stability Main results Main results are presented in the first chart DEMETRA User Demetra User Manual final version4 doc 104 DEMETRA User Manual summar
177. ries with Revised Annual Totals Table D12 Final Trend Cycle Table D12A Forecast of Final Trend Component Table D13 Final Irregular Component Table D13U Irregular component excluded outlier effects Table D16 Seasonal and Calendar Effects Table D16A Forecast of Seasonal and Calendar Component Table D18 Combined Calendar Effects Factors Part E Components Modified for Large Extreme Values Table E1 Raw Series Modified for Large Extreme Values DEMETRA User Demetra User Manual final version4 doc 193 DEMETRA User Manual Table D2 SA Series Modified for Large Extreme Values Table E3 Final Irregular Component Adjusted for Large Extreme Values Table E11 Robust Estimation of the Final SA Series 9A Spectral analysis Definition of the periodogram The periodogram of the series y is computed as follows 1 The y is standardized t lt n t 1 Y n M 9 n y y __ y 2 The periodogram is computed on the standardized z 2 I 4 r Cr A S A where C A Y cos Ar z and A Y sin Ar z Periodogram at the Fourier frequencies The Fourier frequencies are defined by 27 n A 0 lt j lt on H DEMETRA User Demetra User Manual final version4 doc 194 DEMETRA User Manual If the z are iid N O 1 it is easy to see that the corresponding quantities I A are iid x 2 We have indeed t
178. rly series 1 292 1 850 2 128 default 0 280 10A Revision histories Revisions are calculated as a difference between the first earliest adjustment of an observation computed when that observation is the final period of the time series concurrent adjustment denotes as and a later adjustment based on all data span most recent adjustment denotes as A DEMETRA User Demetra User Manual final version4 doc 197 DEMETRA User Manual In case of multiplicative decomposition the revision history of the seasonal adjustment from time N to N is a sequence of R calculated in a following way A A Ri 100x tlN tlt tlt The revision history of the trend is calculated in a similar way Digg ak Riy 100x tlN tlt tlt With additive decomposition R is calculated in the same way if all values A have the same sign 8 Otherwise differences are calculated as R A tIN 4N A tlt The analogous quantities are calculated for final Henderson trends 11A Sliding spans Each period month or quarter which belongs to more than one span is examined to see if its seasonal adjustments vary more than a specified amount across the spans Seasonal factor is regarded to be unreliable if the following condition is fulfilled Ss Max zen S k min y S k gt 0 03 min y S k Where S k the seasonal factor estimated from span k for month t N k period t is in the k th span
179. rmation i e the type date and coefficients of outliers are specified in node Pre processing Tramo Estimation span 1 1999 2 2011 Series has been log transformed No trading days effects No easter effect 3 outliers detected Second part of Main results presents the variance of the white noise innovation for each component extracted by Seats procedure from the observed time series x Observed time series x follows an Arima model of the type 0 B x w B a where a is a white noise variable DEMETRA User Demetra User Manual final version4 doc 127 DEMETRA User Manual with variance V a The residuals a from this model are also called innovations because they are the new unpredictable at t 1 part of x They are estimators of the one period ahead forecast error of the observed series x Seats decomposes a time series into four different orthogonal components These components are trend seasonal transitory and irregular For additive decomposition original time series can be presented as a sum of the components x Sx i Each component follows the general Arima model 0 B x W B a where i trend seasonal transitory or irregular components respectively a WN 0 V a assumed an i i d white noise innovation of i component It is also an estimator of the 1 period ahead forecast error of component i 6 B B w B y B The polynomials 0 B B and B
180. s 2 Jr DATAxs 14 Algeria 3 Morocco 4 EXPORTS IMPORTS CIF IMPORTS CIF1 Tunisia 7 Name IMPORTSCIF Source XCLPRVDR Statistics Time span 1 1957 to 6 2009 197 1 19 1960 01 1980 01 2000 Then the methods can be selected single analysis wizara OO y Choose a series Choose a method x Choose a specification After that the user can choose the specification from the list available in the very top of the window or create new specification In the example below the RSAO specification will be used for seasonal adjustment Obviously the user can define the new specification New Spec option The specification parameters depend on the method TramoSeats or X12 chosen in the previous step For X12 please refer to 4 1 TramoSeats specification is described in 4 2 DEMETRA User Demetra User Manual final version4 doc 83 DEMETRA User Manual Choose a series Choose a method Choose a specification Finishing The specification contains all the Function Jam None no transformation of data Log takes logs of data Auto the program tests for the logdevel specification Finally click the Finishing item and decide if you want add it into Workspace Ee x Choose a series Choose a method Name TramoSeatsDoc 12 Choose a specification Finishing You can choose the name of the processing and decide to add it t
181. s clearly divided into several panels 10 xi Workspace Seasonal adjustment Tools Window Help Browsers A X Xml Excel Tsw usce New Open Save Paste PP Pr rr rr The key parts of the application are e the browsers panel left panel which presents the available time series e the workspace panel right panel which shows information used or generated by the software e a central blank zone that will contain actual analyses e two auxiliary panels at the bottom of the application the left one TSProperties contains the current time series from the browsers panel and the right one Logs contains logging information Those areas will be described in the next paragraphs Panels can be moved resized superposed and closed depending on user s needs The presentation is saved between different sessions of Demetrat The application can contain multiple documents Depending on the preferences the user can present them in different tabs taking the full space default or in floating windows choose this one to follow different steps The main menu item Window gives access to that functionality 4 Closed panels can be re opened through the main menu commands Workspace gt View gt DEMETRA User Demetra User Manual final version4 doc 13 DEMETRA User Manual Time series can be dragged and dropped between windows next section presents
182. s of no month quarter effect is not rejected37 37 http support sas com onlinedoc 913 DEMETRA User Demetra User Manual final version4 doc 110 DEMETRA User Manual In the example above p value is 0 0000 so the null hypothesis is rejected and it could be assumed that seasonality is present e Kruskal Wallis test The second test for stable seasonality provided by Demetra is the Kruskal Wallis test Kruskall VWallis test Kruskal Wallis statistic 162 5477 Distribution Chi2 11 P Value 0 0000 Stable seasonality present at the 1 per cent level In the example above the outcome of the test is stable seasonality present This outcome confirms the result from Friedman test e Test for the presence of seasonality assuming stability Test for the presence of seasonality assuming stability uses the following decomposition of the 2 o GD 2 variance S S t SR where k Nj S gt Xi X j l i l the total sum of squares k 82 Yon Ay X J II p variance of the averages due to seasonality kN 7 S F S XG Xsj j l i l the residual sum of squares The test statistics is calculated as S F Ka F k 1 n k 2 R n k where K 1 and n k are degrees of freedom The example is shown below DEMETRA User Demetra User Manual final version4 doc 111 DEMETRA User Manual Test for the presence of Smo sasres oepees of tedon Mean sare Between mons
183. s used for detailed analysis of the time series The second option called multi processing see 4 2 is a convenient tool for mass production of seasonally adjusted time series 4 1 X12 specifications The X12 specification is to a very large extent organized following the different individual specs of the original program taking into account that peripheral specifications or specifications related to diagnostics are handled in a different way The different parts of the specification are presented in the order in which they are displayed in the graphical interface of Demetra Details on the links between each item and its corresponding X12 spec argument are provided in the following paragraphs For an exact description of the different parameters the user should refer to the documentation of the original X12 program 4 1 1 General description ltem __ X12 spec file General options for the processing Transformation of the original series calendar not specifically related to calendar Automatic modeling Automatic model identification Arima modeling Outliers detection Automatic outliers detection Options on the estimation procedure of the RegArima model Decomposition X11 x11 forecast X11 decomposition DEMETRA User Demetra User Manual final version4 doc 49 DEMETRA User Manual Ze BasIc ee nma a Individual spec arguments Comments OOOO Pre processing Enable Disable the other individuals specs except
184. se between tree pre test options e Add e Remove e None Trading days and holiday adjustments may be obtained from RegArima part or from irregular regression models When the user chooses the Add easter is only added in the variables part of the DEMETRA User Demetra User Manual final version4 doc 52 DEMETRA User Manual Comments a e spec regression spec An automatic identification of the Easter length between 1 8 and 15 days is executed When one chooses the Remove easter is added in the variables and in the aictest parts of the regression spec The specified length of the Easter effect is used When one chooses the None easter is only added in the variables of the regression spec The length of the Easter effect specified by the user is used The length of the Easter effect can range from 1 to 20 days It should be noted that the Length option is hidden when the Add pre test option is active Pretest regression aictest Pretest the significance of the Easter regression variables using AICC statistics Length regression easter w Duration of the Easter effect w length in days of the Easter effect The parameter is active if the aictest None The current version of Demetra doesn t allow the use of stock trading days Pre defined calendar day for the handling of Labor Day and of Thanksgiving are not available see 3 1 1 for list of pre defined holidays Nevertheless the user is
185. seasonal filt Automatic henderson f True Henderson fiter l 3 Details TEE filters seasonalmal Details on specific seasonalma for the dif jods l0 x Data transformation Estimation span 1 1990 8 2009 Series has been log transformed Series has been corrected for leap Model adequation Number of effective observations htenber of estimated parameters ikKelihood 5643055 sformation adjustment 1021 sted loglikelihood 456 3463 dard error of the regression M 936 6925 936 1782 OTT 5786 ramo definition 7 6494 an Quinn 953 1979 This option could be useful if for some periods seasonal pattern changes faster slower than for the others The evaluation can be made using IS ratio chart If for the particular time series the multi processing hasn t been executed yet option Mixed is not available as Demetra needs information about time series frequency In such case Demetra displays the following warning Specifications X12Doc 11 Details on EEr ER Automatic henderson filter DEMETRA User Demetra User Manual final version4 doc 167 DEMETRA User Manual The Mixed option is unavailable for single processing 4 4 3 Period to period data production Multi processing is designed for regular production of the seasonally adjusted data For this purpose the user should define multi processing using the data from the browsers i e Me
186. servations from the sample A within the whole k sample of n gt 7 observations j l Under the null hypothesis the test statistic follows a chi square distribution with k 1 degrees of freedom DEMETRA User Demetra User Manual final version4 doc 202 DEMETRA User Manual e Test for the presence of seasonality assuming stability The test statistics and testing hypothesis are the same as for Friedman stable seasonality test The test statistics is calculated for final estimation of the unmodified Seasonal Irregular Component in case of X12 this series is presented in table D8 e Evolutive seasonality test Moving seasonality test The test is based on a two way analysis of variance model The model uses the values from complete years only For the seasonal irregular component it uses one of the following models depending on the decomposition s type Multiplicative ST X b m e Additive X b m e Where m refers to the monthly or quarterly effect for j th period j k where k 12 for monthly series and k 4 for quarterly series b refers to the annual effect i i 1 N where N is the number of complete years e represents the residual effect The test is based on the decomposition S S S S where eam X the total sum of squares Me II II s 5 k X ej X the inter month inter quarter respectively sum of squares
187. sible to detect all types of outliers only AO additive outliers and TC transitory change or only AO and LS Default critical Others V When Use default critical value is false the value outliers procedure uses the critical value imposed by the user Otherwise the default is used the first case corresponds to critical xxx the second corresponds to a spec without the 24 Initial values are described in the Annex Chapter 6A DEMETRA User Demetra User Manual final version4 doc 76 DEMETRA User Manual TramoSeats Comments Individual spec Argument critical argument It should be noted that it is not possible to define different critical values for different outliers types outliers procedure outliers regressor EML Others True if exact likelihood estimation method is estimation outliers used false if fast Hannan Rissanen2 gt method is used ls enabled E Outliers detection span Selection type Option Defaut critical value Critical value EML estimation TC rate aio Describes the outliers considered in the automatic outliers detection AO additive outlier LS level shit TC transitory change 4 2 8 Estimation TramoSeats Comments Individual spec Argument EML estimaton Arima model type True if exact maximum likelihood for SEATS others and TRAMO is used false if least squares conditional for seats unconditional for tramo is used Precision used in the optimiz
188. space E Eal wWwokspace_ ld Single processing gt TramoS eats a Multi processing d Specifications E TramoS eats Open Exclude Delete That specification called active specification will be used to generate the processing This specification can be changed at any time When the user double clicks a series in a browser the software follows the following logic If there is an active specification in the workspace panel then Laem trad If some single processing are open i e single processing windows have been opened in the central panel they are updated with the new series iho ins pee Seasonal adjustment TramoSeatsDoc 1 Tools Foss 8 4 Ymi Excel Tsw ust 3 W tramoseatsDoc 1 derw Window Help 0 01 1800 O1 24 0 01 2000 If no unlocked single processing is available a new one is generated with the active specification DEMETRA User Demetra User Manual final version4 doc 80 DEMETRA User Manual The other option is to drag any specification from the workspace panel and drop it in the central panel of the application A new single processing window will open automatically Deere tra 4 Workspace Seasonal adjustment X1fOoc 2 Tools Window Help roses lt lt x Xm Exe Tsw ust g ae 7 wr drag drop a specification node The data can be imported into specification s window either by a double clic
189. ss covariance function As fA F A f A gt 0 MMSE yields correlated estimators Nevertheless cross correlations estimated by TramoSeats tend to zero as cross covariancies between component s estimators and estimators are finite when at least one non stationary component exists The ACGF for the stationary transformation of component 0 B s that follows the model 0 B 0 F 0 B s W Bay is a e F a The final MMSE estimator of seasonal component follows the model s V B F x As Bee B o B 0 B 0 F B F OB OF innovations in original series B O F 9 B Q F _ l p B O F i v B F k the final estimator can be expressed in terms of the B s k ACGF of theoretical final estimator is calculated as _ a B a F BLE Sy y where a B 0 BY 9 B 6 B F 0 F 9 F 6 F P B p BYOB PCE 9 F OF 91 D CANETE A MARAVALL 2011 DEMETRA User Demetra User Manual final version4 doc 188 DEMETRA User Manual Via ja V a ks ACGF can be also presented as a following function n y BI F j l where p correlation between observations separated by lag J The spectrum can be obtained from ACGF function by applying Fourier Transform 2 e PsiE weights Estimator of seasonal factor is calculated as St v B F x O B O B By replacing x a seasonal factor can be expressed as V B FP
190. ssanen algorithm Hannan Rissanen algorithm 2 is a two step procedure for the selection of appropriate orders for the autoregressive and moving average parameters of the ARIMA model In a first step a high 81 Backshift operator B is defined as By y _ It is used to denote lagged series 82 HANNAN E J and RISSANEN J 1982 NEWBOLD D and BOS T 1982 DEMETRA User Demetra User Manual final version4 doc 183 DEMETRA User Manual order AR m where m gt max p qg model is fitted to the time series X Then the residuals ax from this model are used to provide estimates of innovations in ARMA model E X aX k 1 In the second step the parameters p and gof the ARMA model are estimated using a least squares linear regression of X onto X _ X _ 5 15 _ for combination of values p and q Finally Hannan Rissanen algorithm selects a pair of p and q values for which gt ptq logT a log is the smallest The advantage of Hannan Rissanen algorithm is a speed of computation in comparison with exact likelihood estimation Signal extraction in Seats e Estimation procedure The model based signal extraction procedure consist of estimating the seasonally adjusted time series by means of the Wiener Kolmogorow filter as the Minimum Mean Square Error estimators using UCArima unobserved component Arima model Seats decomposes a series x received k from Tramo into components x x a E
191. ssumed for the central observations of the series Symmetric and centered filter allow to avoid phase effect The filter can be expand in the following way A M0 6 PaO gp PU PO er E t 1 A When T lt t k observations at the end of time series that are necessary to calculate x are not available yet so the filter cannot be applied Because of that needed future values are replaced by their optimal forecast from ARIMA model on x The estimator that uses such forecasted values is called preliminary estimator As the forecasts are linear functions of present A and past observations of x the preliminary estimator of xi obtained with the forecasts will be a truncated filter applied to the x This truncated filter will not be centered nor symmetric As a result the phase effect occurs e Wiener Kolmogorow filter and ACGF function Wiener Kolmogorow filter shows the weights with which the each component s innovation A contribute to the estimator Xinr These weights provide the moving average expressions for the revisions For the two component model s seasonal component n non seasonal component in the frequency domain Wiener Kolmogorow filter V B F that provide the final estimator of s t is expressed as the ratio of the s t and x t pseudospectra The spectrum of the estimator of the seasonal component is expressed as 86 MARAVALL 1998 87 KAISER R and MARAVALL A 2000
192. stant Others term is part of the Arima model it highly depends on the chosen model P D Q BP BD Arima model P D Q BP Parameters of Box Jenkins Arima model BQ Arima BD BQ init P D QO BP BP BQ dimension P regular autoregressive order D regular differencing of order D Q regular moving average order BP seasonal autoregressive order BD seasonal differencing of order BD BQ seasonal moving average order theta btheta Arima model th jgr theta initial fixed values2 for regular Arima moving average parameters parameters bth jqs btheta initial fixed values for seasonal Arima fixed moving average parameters parameters phi bphi Arima model phi jor phi initial fixed values for nonseasonal Arima autoregressive parameters parameters bphi jos bphi initial fixed values for seasonal Arima fixed moving average parameters parameters Imputation of initial values of parameters in Demetra is the same for TramoSeats and X12 For description refer to 3 2 7 4 2 7 Outliers detection a Comments IsEnabled Others jatip Presence or not of the outlier individual spec outliers Outliers Others int1 int2 Span used for the outlier detection The span detection outliers can be computed dynamically on the series for apan instance Excluding last 12 obs Others aio Describes the outliers considered in the outliers automatic outliers detection It is pos
193. stributional assumptions It uses the rankings of the observations Seasonal adjustment procedures uses Friedman test for checking the presence of seasonality Friedman test is called a stable seasonality test This test uses preliminary estimation of the unmodified Seasonal Irregular component for X12 this time series is shown in table B3 from which k samples are derived k 12 for monthly series and k 4 for quarterly series of size N N N respectively Each k corresponds to a different level of seasonality It is assumed that seasonality affect only the means of the distribution and not their variance Assuming that each sample is derived from a random variable x following the normal distribution with mean m and standard deviation oO the following null hypothesis is tested H m m m against H m m for the least one pair p q The test uses the following decomposition of the variance YY x x n x x Va i j l i l ia where x is the average of j th sample The total variance is therefore broken down into a variance of the averages due to seasonality and a residual seasonality 101 Unmodified Seasonal Irregular component is the seasonal irregular factors with the extreme values DEMETRA User Demetra User Manual final version4 doc 201 DEMETRA User Manual The test statistics is calculated as k 2 D nj Aj Xe j l Ff 1 F k 1 n k D2 aa j l i l n k Wher
194. sults of the test Pr gt val Demetra default setting lt 0 01 0 01 0 11 o Independence test The independence test is the Ljung Box test see the Annex section 12A which is distributed as X k np where k depends on the frequency of the series 24 for monthly series 8 for quarterly series 4 freq for other frequencies where freq is a frequency of the time series and np is the number of hyper parameters of the model number of parameters in the Arima model Results of the test Pr X k np gt val Demetra default setting 0 01 0 11 O Spectral test Demetra checks the presence of the trading days and seasonal peaks in the residuals using the test based on the periodogram of the residuals The periodogram is computed at the so called Fourier frequencies Under the hypothesis of Gaussian white noise of the residual it is possible to 35 In future versions of Demetra it will be possible to choose the definition of the residuals that must be used in the tests and displayed in the graphical interface Obviously the choice is more a question for purists DEMETRA User Demetra User Manual final version4 doc 108 DEMETRA User Manual derive simple test on the periodogram around specific groups of frequencies The exact definition of the test is described in the Annex section 12A Results of the test P stat gt val Demetrat default setting lt 0 001 0 001 0 01 0 01 0 11 e R
195. t for the sliding spans analysis for seasonal component is presented The user should be aware that an unstable estimate of a month s seasonal factor can give rise to unstable estimates of the two associated month to month changes Because of that in majority of cases more months are flagged for unreliable month to month changes than for unreliable seasonal factors The first panel shows the sliding spans statistic obtained for each period This statistic calculates the maximum percentage difference in the seasonal factors for period month or quarter t The estimation of seasonal component is regarded as unstable if statistic is greater than 3 The exact Statistic s formula is given in the Annex section 11A 43 FINDLEY D MONSELL B C SHULMAN H B and PUGH M G 1990 DEMETRA User Demetra User Manual final version4 doc 120 DEMETRA User Manual 0 04 0 03 0 02 0 04 0 01 1999 01 2000 01 2001 01 2002 01 2003 01 2004 01 2005 01 2006 01 2007 01 2008 01 2009 The next panel presents the cumulative frequency distribution of the sliding spans statistics months or quarters using frequency polygon On the horizontal axis values of the sliding spans Statistics are shown while vertical axis presents the frequency in percentages of each class interval 4 The example below shows distribution where the first label on the X axis is 0 0025 This represents an interval extending from O to 0 005 This interval has a frequen
196. t the estimation of the seasonal component and because of that it should be appropriately modeled2 The S ratio chart also reveals the periods with more statistical variability than typical periods i e typical variability for specific time series If the S ratio seem to be very erratic the seasonal factors will be erratic too The seasonality is expected to be relatively stable so in case of high variability of seasonal component the user should choose a longer moving average for its estimation Changes in seasonality over time are acceptable unless there is a noticeable change from below to above the overall mean or vice versa The overall mean is equal to 1 in case of additive model and O in case of multiplicative model The problem is illustrated with the chart below The S I ratios for majority of periods are highly unstable For some of them e g S I ratios for July August September the effect of seasonality on time series changes from positive to negative On the contrary the values of the seasonal component for April indicate that for this period in the beginning of the time series the seasonally adjusted data were higher than raw series while in the end of the period the seasonally adjusted data were smaller than raw series 28 See Guide To Seasonal Adjustment 2007 DEMETRA User Demetra User Manual final version4 doc 93 DEMETRA User Manual 0 8 0 6 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec 4
197. t to Additive If the transformation is set to Auto Mode is automatically set to Undefined When UseForecasts is false maxlead is set to 0 and the x11 procedure doesn t use any model based forecasts Otherwise the forecasts of the RegArima model default airline model if the user doesn t use pre processing see basic options is used to extend the series First parameter of sigmalim lower sigma boundary for the detection of the extreme values Second parameter of sigmalim uppersigma boundary for the detection of the extreme values Specifies which seasonal moving average seasonal filter will be used to estimate the 64 DEMETRA User Manual Individual Argument Comments spec seasonal factors for the entire series The following filters are available13 e Mixed enables to assign different seasonal filters to a particular month or quarter using Details on seasonal filters Option Mixed option available only after executing specifications using multi processing seasonal adjustment see description in section 4 4 2 3 S3x1 3X1 moving average S3x3 33 moving average S3x5 3x5 moving average S3x9 3x9 moving average S3x15 3x15 moving average stable a single seasonal factor for each calendar period is generated by calculating the simple average of all the values for each period taken after detrending and outlier adjustment x11 default 3X3 moving average is used to calculate the
198. tem from the main menu and clicking the Specifications sub menu In the next step the user should make a choice between TramoSeats specification and X12 specification After the user has chosen all the suitable options in the Specifications dialog box the new specification is automatically sent to the corresponding node of the Workspace The new specification will be saved with the workspace for future use It can be later used in the same way as any predefined specification Workspace Seasonal adjustment Tools Window Help en ia Single analysis E Workspace_1 El dam Single processing wwa Multi processing gt TramoSeats x12 pa nuwe Mitiprocessing d Specifications E Anma modelling td aE Tramo Seats Outliers detection False i e RSAO Estimation oio o i Decomposition Seats RASA5c S i Calendars _ Default N User defined variables 8 Description from CAPORELLO G and MARAVALL A 2004 DEMETRA User Demetra User Manual final version4 doc 48 DEMETRA User Manual The next two sections contain valuable information about the specifications The description of X12 specifications is presented in 4 2 and a description of TramoSeats specifications is presented in 4 3 Demetra is able to perform seasonal adjustment for one single time series as well as for the whole set of time series The first option is called single processing see 4 1 and i
199. the results of Pre processing Estimation span 1 2000 2 2011 Series has been log transformed No trading days effects Easter effect detected 3 outliers detected The message Series has been log transformed is displayed if a logarithmic transformation has been applied as a result of the test done by X12 Otherwise information does not appear In case of X11 RSA1 and RSA3 specifications no trading days effect is estimated For RSA2c and RSA 4c specifications working days effect and leap year effect are pretested and estimated if DEMETRA User Demetra User Manual final version4 doc 89 DEMETRA User Manual present If working day effect is significant pre processing part includes information Working days effect 1 regressor Message Working days effect 2 regressors means that also leap year effect is significant For RSA5 trading days effect and leap year effect are pretested If the trading days effect has been detected message Trading days effect 6 regressors or Trading days effect 7 regressors is displayed depending whether leap year effect has been detected or not If Easter effect is statistically significant in series Easter effect detected is displayed If X11 specification is used or any significant outliers have not been found under other specifications information No outliers found is displayed In this section only total number of detected outliers is visible More information i e type date and c
200. the seasonally adjusted series or irregulars reveals inadequacy of the seasonal adjustment filters for the time interval used for spectrum estimation In this case different model specification or data span length should be considered 39 The theoretical motivation for the choice of spectral estimator is provided by SOKUP R J and FINDLEY D F 1999 DEMETRA User Demetra User Manual final version4 doc 114 DEMETRA User Manual Revision histories Main results Pre processing RegArma Decomposition X11 Diagnostics z Seasonality tests H Spectral analysis H Sliding spans H Model stability It is known that the estimated SA and trend figures change as new observations are added to the end of the original time series The change in the estimated SA and trend values is called revision Revision history illustrates the changes in the seasonally adjusted series and trend series which take place as new observations are added to the end of the original time series The illustrated difference is between the initial estimate marked by a blue circle and the latest estimate red line The difference between those two values is called a revision As a rule smaller revisions are better The revision history is useful for comparing results from competing models When the user defines two seasonal adjustment models for one time series and both these models are acceptable and then revision history can be used for choosing the better m
201. thod Estimation Processing Priority Quality Y 12 1899 In this case Demetrat saves the location of the file from which the data come from If the variables in multi processing come directly from external source e g they are copied from Excel and pasted directly into Processing window it won t be possible to update the processing Such variables are static so their location is not saved by Demetra Data can be copied from Exel and pasted into Demetra multiprocessing window using Copy Paste options The variables will not be added into the Browser see picture below DEMETRA User Demetra User Manual final version4 doc 168 DEMETRA User Manual PTs 2 ticrosoft Excel HICP m_to_mods lo xi Workspace Seasonal adjustment SAProcessing 1 Tools Window Help E pik Edy a Widok wstaw Format Narzedzia Dane Okno Pomoc f X Browsers x CENS OSA BIG RIF HB B F 9 81 fly 100 Bap Xml Excel T Tsw us 4 gt f zi un ta u a o a wi By gal edz ze zmiana Jei XI2 RS 01 02 1996 01 03 1996 All items HICP Package holiday Accommodation services 15 0 7 1 7 01 04 1996 01 05 1996 01 06 1996 01 07 1996 01 08 1996 01 09 1996 01 10 1996 01 11 1996 01 12 1996 01 01 1997 01 02 1997 01 03 1997 01 04 1997 01 05 1997 ar Rysuj Lg Autoksztatyy a 1 4 eh gl amp AA Zaznacz obszar docelowy i nacisnij EM Suma 6323219 NUM h 2 2 2 pa 1 DEBUG Demet
202. tion de boissons 0 X12 R5 Concurrent Walid 6 Good basic checks Fabrication de produits E b X12 R5 Concument Walid 10 Good definition Good 0 000 Fabric cation de pam a Concurrent Valid Fi annual totale Good Concurrent Valid 6 0 007 Concurrent Valid i Concurrent Valid 6 Visual spectral analysis Concurrent Valid 6 spectral peaks Transformation Concurrent Walid 6 Good Travail des grai Concurrent Valid 6 spectral td peaks Good Log based es idual Level based normality Bad 0 001 gt aT independence Good a ii de produits de boulangerie patisserie et de pates al 01 1994 01 18 01 2002 01 2004 01 2006 01 2008 01 2010 01 1990 01 1992 01 1996 DEMETRA User Demetra User Manual final version4 doc 175 DEMETRA User Manual 4 5 Additional functions 4 5 1 Changing the specification The user is able to modify the specification that is currently used for processing and to see immediately the result of changes made The specification could be edited through the main menu TramoSeatsDocxxx X12Docxxx gt Specification It is possible to edit the specification used to generate the processing current specification or the specification that corresponds to the results result specification Current specification is displayed in a non modal dialog box so the user can change any option and inspect its impact on the results For a detailed description of the specifications the user should ref
203. tliers including AO additive outliers LS level shifts TC transitory changes using default critical values Airline model an Airline model 0 1 1 0 1 1 is estimated Automatic model identification Demetra identifies and estimates the best Arima model 4A Model selection criteria Model selection criteria are statistical tools for selecting the optimal order of the ARMIA model The basic idea behind all these criteria is to obtain much explanatory power measured by the value of the likelihood function with only a few parameters The model selection criteria penalise for using many parameters and rewarsd for a high value of the likelihood function Some of the most known information criteria are Akaike Information Critera AIC Corrected Akaike Information Critera AICC Hannan Quinn Information Critera HannanQuinn and Schwarz Bayes information criterion BIC The formulas for model selection criteria are AIC 2L 2n n 1 AICC 2Ly 2n 1 x HannanQuinny 2L 2n loglog N BICy 2Ly n log N Where N number of observations in time series n number of estimate parameters Ly loglikelihood function For choosing Arima model parameters Tramo uses B C criteria with some constrains aimed at increasing the parsimony and favoring balanced models i e models with similar AR and MA values80 For each model selection criteria the model with smaller value is preferred 80 G
204. troduced a with first lag l and last lag 1 Demetrat 22 The user can find more details and examples in MARAVALL A 2008 DEMETRA User Demetra User Manual final version4 doc 72 DEMETRA User Manual TramoSeas Individual Argument Comments spec estimates the following regression model for this variable Var p x t l 6 x t 1 To estimate Var p x t L The user should put first lag last lag 1 If put first lag 0 and last lag 12 it means that in addition to instantaneous effect the effect of variable Var is spread over one year Example Pre specified outliers Tra moses 3 x Pre specified outliers x Is 7 2002 Year 2010 ao i Peiod 5 Type Example Ramps TramoSeatsSpec 3 xj Ramps RampProperties x DEMETRA User Demetra User Manual final version4 doc 73 DEMETRA User Manual Example Intervention variables TramoSeatsSpec 3 xj Sequences Sequences of ones InterventionSequenceProperties xj _Add_ _Remove 2 05 0 Start 2002 02 01 End 2002 05 01 Cancel _ o Example User defined variables TramoSeatsSpec 3 Intervention variables User defined variables RegVarProperties xj pan r paps Var 1 A x 4 2 5 Arima modelling automatic modelling TramoSeats Comments Individual spec Argument IsEnabled Others inic idif Presence or not of the automdl individual Automatic spec mode
205. u of the Census http www census gov srd www x12a x12down_pc html DEMETRA User Demetra User Manual final version4 doc 209
206. ue 1 TramoSeatsDoc 2 2X12Doc 1 4 Orange 5 Vista Documents Documents option offers some additional options helpful for organising windows The left panel contains the list of all windows currently displayed in central panel of Demetra On the right activate close buttons and a presentation styles are available TramoSeatsDoc 2 Activate E_E o Tile Horizontally Tile Vertically Cascade Arrange Icons Close DEMETRA User Demetra User Manual final version4 doc 47 DEMETRA User Manual 4 Seasonal adjustment Demetra provides two methods of seasonal adjustment TramoSeats and X12 For both methods a list of pre defined specifications is available using the naming conventions of TramoSeats This list contains the most commonly used specification for seasonal adjustment Pre defined specifications correspond to the terminology used in TramoSeats and are described in the Annex section 3A The default specifications appear in the Workspace tree The users are strongly recommended to start their analysis as explained below with one of those specifications usually RSA4c or RSA5c for X12 and RSA4 or RSA5 for TramoSeats and to change afterwards some of the options if need be For more advanced users Demetra offers an opportunity to create the new specifications for seasonal adjustment and to add them to the list This could be done by choosing the Seasonal adjustment i
207. ult DEMETRA User Demetra User Manual final version4 doc 164 DEMETRA User Manual As an example the following panel shows how to change the pre specified outliers EE X12 RSA5c Dwellings competed Apply Restore Save p 0 000 Dalal 0 063 Jan Mar May Jul Sep Now Feb Apr JunAug Oct Dee When the new options are chosen the user should click on Apply button to launch the seasonal adjustment with modified settings The user can save the new settings and results using Save button The multi processing will contain then the modified specification for that series Otherwise the user can come back to the previous settings using Restore button DEMETRA User Demetra User Manual final version4 doc 165 DEMETRA User Manual It is not necessary to close the details window to get information on another series that window is updated by a simple click on another series of the multi processing view It is also possible to create a separate single processing from a multi processing document by dragging the corresponding item from the series column to the central panel of Demetra Demetra allows the user to accept the models the quality of which wasn t satisfactory If the user clicks on the Accept option Demetra changes the message displayed in Quality column into
208. ults of the tests of assumptions made by Seats In particular seas variance and irregular variance show the probability value of a test to check whether the variance of estimators of the seasonal component and of the irregular component respectively is close to the variance of their actual estimates The third test seas irr cross correlation checks theoretical crosscorrelation between estimators and empirical cross correlation between estimates seats seas variance Good 0 732 irregular variance Good 0 254 seas irr cross correlation Bad 0 031 For each of three tests three different results are possible Bad means that the test statistics is significant at 1 level Uncertain means that the test statistics is significant at 5 level and Good means that the test statistics is not significant at 5 level Uncertain or bad results for seas variance may evidence over under adjustment for crosscorrelation may evidence too much correlation Additional information is available in three subsections Charts Table and S I ratio In Charts section the user will find e the original series with forecasts e the final seasonally adjusted series e the final trend with forecasts e the final seasonal component with forecasts e the final irregular component e the final seasonal component with forecasts The same time series are presented in Table section The final estimation of the seasonal irregular component and final se
209. vation obtained by applying the adjustment procedure to a sequence of three or four overlapping spans of data all of which contain this observation 2 Each period month or quarter that is common to more than one span is examined to see if its seasonal adjustments or some related quantities vary more than a specified amount across the spans 40 A seasonal break is defined as a sudden and sustained change in the seasonal pattern of a series The presence of this event is reflected in SI ratio A seasonal brakes are unwanted feature of time series as the moving averages used by X12 are designed to deal with series which have a smoothly evolving deterministic seasonal component plus an irregular component with stable variance If there is a seasonal break in the series it will be reflected in SI ratios 41 The following casus are mentioned in Guide to Seasonal Adjustment 2007 Fast moving seasonality means that the seasonal pattern displays rapidly evolving fashion from year to year 42 The procedure of withdrawing spans from time series is described in FINDLEY D MONSELL B C SHULMAN H B and PUGH M G 1990 as follows To obtain sliding spans for a given series an initial span is selected whose length depends on the seasonal adjustment filters being used A second span is obtained from this one by deleting the earliest year of data and appending the year of data following the last year in the span A third span is obtained fr
210. xml files e settings for presentation the diagnostic where the user can change the critical values and other parameters for diagnostic tests e outputs where the folder that will contain the results is specified Those functions are discussed below WorkSpace This node enables the user to switch on off auto loading of the last workspace and to choose the colour for the active item in the Workspace panel By default the active item is blue Here the change to red was made DEMETRA User Demetra User Manual final version4 doc 37 DEMETRA User Manual A F Specifications AF Tramo Seats 3 RSAO 7 RSA 2 Es a a E 4 RSAZ 5 ed RSA H Diagnostics Wous g LJLJ LI LIL amp Pd Default SA processing output The user can decide which parts of the results will be presented after seasonal adjustment SA processing To do it for each SA method the user can show or hide the items from the list of results By default all items are displayed after SA processing The picture below presents that two diagnostics will not be visible in the SA results from TramoSeats Tramo Results Kolekcja H X12Resul ts Kolekcja H a q Elf Main results Click here to open 7 Charts Show Hide result D Table panel for TramoSeats cc Pre processing Tramo AO Revisions history E Sliding spans Hf Model stability OK Caed DEMETRA User Demetra
211. y Good basic checks definition Good 0 000 annual totals Bad 0 063 spectral seas peaks Good spectral td peaks Good normality Good 0 740 independence Good 0 927 spectral td peaks Uncertain 0 098 spectral seas peaks Bad 0 003 residual seasonality on sa Good 0 606 on sa last 3 years Good 0 926 on irregular Good 0 671 outliers number of outliers Good 0 014 m statistics q Good 0 437 gq without m2 Good 0 455 A description of tests presented in the Diagnostic panel is presented below e Basic checks The first section includes two quality diagnostics definition and annual totals o Definition This test is inspecting some basic relationships between different components of the time series The following components are used in formulas that are tested y _f Original series sss yc _f Interpolated series Y with missing values relaced by their estimates To HI Trend without regression effects si _f Seasonal without regression effects A Jil Irregular without regression effects 34 The names mentioned in the document appear in the graphical interface of Demetra The corresponding codes are used in the csv output For compatibility issues with previous versions they have not been aligned on the names For some series it is possible to generate the forecasts computed on 1 year the corresponding code is defined by adding the _f suffix for example y becomes y_f
212. y the layout x Save sa seres Save calendar comected senes Save seasonal component Save trend Save iregular component If the user will set the option layout to ByCompenent the output will be generated in the following Way DEMETRA User Demetra User Manual final version4 doc 41 DEMETRA User Manual A C D Unempoyment rate Dwellings competed 9916 368 10498 27 10747 64 11737 07 12476 14 1244096 11767 94 01 01 1991 01 02 1991 01 03 1991 01 04 1991 01 05 1991 01 06 1991 f 226337962 T 672831005 6225091611 6 o00014 1 01 07 1991 9 44469119 11 08 1994 go I sA 5 Org fark Ee ll al nl ea Ti l4 d F Components are placed in the separate sheets Gotowy The option OneSheet will produce the following xls file T demetra xis tl B D E F ee rllla ld d F ODBC 04 17 1991 iUnempoyment rate Orig 01 01 1991 01 02 1991 01 03 1991 01 04 1991 01 05 1991 01 06 1991 01 07 1991 01 08 1991 01 09 1991 01 10 1991 01 11 1991 7 3 75 7 9 8 6 9 6 10 1 10 7 11 1 11 4 arkusz1 b Series Arkusz1 g 0 073662 0 17283 0 32509 0 1868 0 155109 0 170372 0 09329 0 08194 0 09951 0 074272 7 226338 T 6 2031 6 r001 9 444691 9 929628 10 60671 11 18194 11 49951 Dwellings competed Ong 6626 6239 T1f3 6586 6 24 11795 10358 8618 10104 10712 12695 30960 Ia 0 890044 0 784796 0 667402
213. y transformation This node is divided into tree sections e Variance In this section the variances of the stationary transformation of the components column Component variances of theirs theoretical estimators column Estimators and variances of theirs empirical actually obtained estimates column Estimate are displayed see also section 4 3 2 2 1 Variance OOOO Component Esmar Estimate O Pv 0 0024 a e CC 0 8210 seasonal 01730 0 008 franstory 05150 0 3786 0 7450 It follows from properties of model for the estimator that this estimator will always underestimate the component estimators always have a smaller variance than components The size of underestimation depends on the particular model The underestimation will be relatively large when the variance of the component is relatively small It means that for example the trend estimator always has a smaller variance than trend component and the ratio of the two variances get further away from one as the trend becomes more stable Therefore the more stochastic the trend is the less will its variance be underestimated On the other hand the 56 MARAVALL A 1995 DEMETRA User Demetra User Manual final version4 doc 137 DEMETRA User Manual variation of a very stable trend will be extremely underestimated It means that the trend estimator provides a more stable trend than the one implied by the theoretical model For all components

Demetra+ User Manual - CROS

Contents

Download Pdf Manuals

Related Search

Related Contents