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Demetra+ User Manual - CROS

1. Main results double click on the time series o Jr Inseexds 50 Estimation span 1 1990 8 2009 Series has been log transformed Trading days effects 6 variables Decomposition Seats FRANCE Alim et tabac 11 Diagnostics Industries alimentaires 001563038 Transformation et conservation de la viande et pr par Transformation et conservation de fruits et legumes 00 Fabrication dhuiles et graisses v g tales et animales Fabrication de produits laitiers 001563340 trend Innovation variance 0 0097 seasonal Innovation variance 0 0554 Travail des grains fabrication de produits amylac s 0 irregular Innovation variance 0 5019 Fabrication de produits de boulangerie patisserie et de Fabrication d autres produits alimentaires001563349 Fabrication d aliments pour animaux 001563352 Fabrication de boissons 001563041 RSAI Fabrication de produits base de tabac 001564044 RSA2c FRANCE Mat lect 21 Ex FRANCE Mattt i mark the specification FRANCE Textile 9 0 9 RSA5c 01 1990 01 2000 01 20 dente aar kl Salo 7 01 1995 01 2005 EPEA c i Calendars xj The user can inspect the different facets of the results through the exploring tree displayed in the left panel of the output window The results contain many detailed panels The user can go through them by selecting a node in the navigation tree of the X12 processing The curren
2. 500000000 pA Mal VI 01 1970 01 1974 01 1978 01 1982 01 1986 07 1990 01 1994 01 1996 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 They 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 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 to paste it e g into Excel Copy all growth data copies m m growth rates of the time series and allows to paste it e g into Excel Remove all removes all time series from the chart Paste pasties 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 y y growth rates for all time series in the chart DEME
3. Specifications X12Do0c 3 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 o co o a o T o red ho 0 0 Basic AICC Difference Transformation El Trading days _ Calendar effects Type None ynomials Regression E Easter effect in use Arima modelling Is enabled True ular AR 1 0 77611 B 0 39114 B 2 0 17295 B Automatic modellinc Pretest Add isonal AR 1 Peon ular MA 1 fae Muitliars datastian Meaningful information is provided in the Pre processing gt Arima panel or in the different panels of the spectral analysis DEMETRA User Manual doc 122 The X11 panel of the specification dialog box contains a rich set of options on the X11 Decomposition 11 A Tables B Tables C Tables D Tables E Tables Diagnostics Seasonality tests E Spectral analysis Sliding spans DEMETRA User Manual Periodogram Auto regressive spectrum AICC Difference E Trading days Type Non El Easter effect in use Is enabled True Pretest Add Type Type of regression variables decomposition Their effects appear for instance in the Sl ratio chart 1 15 Specifications X12Doc 2 Basic Use forecasts Transformation E 1 General Calendar effects LSigma 1 5 Re
4. double max stats Max min stats Min rmse Math Sqgrt stats SumSquare diff Length 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 Manual doc 144 DEMETRA User Manual REFERENCES BOX G E P and TIAO G C 1975 Intervention Analysis 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 Espa a 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 pu
5. they might lead to larger discrepancies We consider the ARIMA model P B A BY Vorig X orig h H OBE or after differencing B y XB u O B e We consider that we have n observations after differencing and k regression variables Without going into all the mathematical details of the problem below we shortly describe the different solutions2 1 1 TramoSeats Tramo uses the following algorithm 1 Filter the differenced exogenous variable by means of the Kalman filter We get y y where L corresponds to the lower triangular matrix of the Cholesky decomposition of the covariance matrix of the model 2 Filter the differenced regression variables including the additive outliers corresponding to missing values by means of the Kalman filter We get X L X 3 Solve by OLS the linear regression y X 6 n 4 The OLS is solved by using the QR algorithm and the residuals are obtained through that procedure see appendix 2 for further information on OLS estimation by QR decomposition 29 All estimations are based on the model after differencing so that the noises are stationary ARMA processes DEMETRA User Manual doc 125 DEMETRA User Manual The procedure provides n k independent residuals However the relation to the time of those residuals is not obvious after the QR decomposition so that the some tests like periodograms should not be used To get round that problem Tramo also provi
6. 4422 M ktkprocessine MONU Sc dccerccecstrtbdivaitd atari ondeerddaentebatntdaetbadeeeewavenes 113 4223 IDE TANGO tresu necra a erates ee ie eee eee 114 4 5 Period to period data ProductiOn cccccsscccssecccssecccesccceecceseneceeenecesenceseuecessecessecessueeeeens 117 4 6 Sending the results to external GeVICOS sirr A T bles cae 120 S JAGOIGION al TUNGE ONS sorne EINE 121 5 1 Changing the SPeCifiCallOn sicceshisases aide cessenccaeeasieveteusaieitaiausteilooveebadorida sessed easiee 121 5 2 Saving and refreshing WOrKSPaCES ccccccsssccccessececcessccceausececeauececeeeseceseueceeseaeeeseusesetseneces 123 NG A Seae Cee Retro Ean a ETE Tre ann eae ME ann en en ee ey ener ame eee eer ere sete 125 1 DETINITION OF the residual Scenie a tupdareesbateannteeds 125 LL TINFATNIO SCAUCS onsa aa a E a N N 125 1 2 a CATAE OE E A E EE EEEN ssp vasa AE suas AOE A A A een aaa 126 1 3 Demetra Fecosas iaaa A N NN 127 1 4 lie FOUR K anaa N AA 128 2 Least squares estimation by means of the QR decomposition s sesessssseesesserresrressseee 128 Be SPECE ON oaan a T A eases saperaiae 129 fe WSUS aaa NE NS E vrs anton a ones oNeeRNR 130 4 1 D ornik Hansen testor anaE A N A 130 4 2 UUME BOX MOS eiea O EE 131 4 3 Spectral e lensen ewaadaiaanenaneticatnasisotanteusenameate ener an onaptemieutak 131 4 3 1 Definition of the periodogram sascicirccscniveiededhovalstecwedeleueansdeasGivasctedvassedmuiesaes een 131 4 3 2 Pe
7. 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 analyse 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 Manual doc 23 DEMETRA User Manual click on header to paste one variable to the browser click on the top left corner cell to paste all variables to the browser wet ee e et et ol ol etl el et oe O a aes 5 5 OOGG fa oe 82 fF oO B88 gt z The 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 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
8. et drag drop a specification node The data can be imported into specification s window either by a double click 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 DEMETRA User Manual doc 67 DEMETRA User Manual i Specifications ia Multi processing gt Wizard 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 output will be generated instantly 4 3 1 2 Creation of a single processing by defining new specifications This function is activated from the main menu i Specifications iat Multi processing In the first step the user should choose the series he she wants to analyse using the browser Single analysis Wizard i xj Choose a series Xml Excel Tsw usce Choose a method ee id gt we New data set xds 2 sie DATAxs 14 He Algeria 3 e Morocco 4 gt EXPORTS gt EXPORTS FOB IMPORTS CIF1 2 Tunisia 7 Name IMPORT
9. o Evaluative seasonal test o Residual seasonality test o Combined seasonality test 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 X 12 ARIMA and to the Annex 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 in a DEMETRA User Manual doc 106 DEMETRA User Manual 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 ia Single analysis Wizard 4 4 1 Defining a multi processing Creation of a new multi processing This option opens the following window E SAProcessino a ioli 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 w
10. 2006 2167 2190 MARAVALL A 1995 Unobserved Components in Economic Time Series in H Pesaran and M Wickens eds The Handbook of Applied Econometrics Oxford 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 SHISHKIN J YOUNG A H and MUSGRAVE J C 1967 The X 11 variant of the Census Method Il 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 Bureau of the Census http www census gov srd www x12a x12down_pc html DEMETRA User Manual doc 146 DEMETRA User Manual DEMETRA User Manual doc 147
11. Both X 12 ARIMA and TramoSeats estimate trading day effects by adding regressors to the equation estimated in the pre processing part RegArima or Seats respectively These regressors 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 other calendars e Chained calendars defined by two other calendars and a break date The calendars can be defined recursively The dialog box allows defining all calendars described above In the column on the right the number of calendars already defined is shown a PropertiesDlg El Rane National calendars Composite calendars Chained calendars DEMETRA User Manual doc 21 DEMETRA User Manual If the user chooses the option National calendars the following window is displayed The user can define new calendar Add button or modify existing one The list on the left contains all national calendars defined by user In the panel on the right the user could specify the successive parameters National calendar Name Pre specified holidays Easter related days Freed d
12. Edit b 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 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 drop them into Selection window DEMETRA User Manual doc 108 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 de
13. components requires that only irregular components include noise ARIMA models estimated for each component are presented below DEMETRA User Manual doc 101 DEMETRA User Manual Model Non stationary AR 1 B B 12 B13 Stationary AR 1 MA 1 0 75112 B 0 88252 B 12 0 66267 B 13 Innovation variance 1 0000 trend Non stationary AR 1 264 B Stationary AR 1 MA 1 0 010354 B 0 96965 B 2 Innovation variance 0 0138 Seasonal Non stationary AR 1 B B 2 B 3 B 4 B 5 86 B 7 B 8 B 9 810 B11 Stationary AR 1 MA 1 0 67206 B 038022 B 2 0 13433 B 3 0 060935 B 4 0 20492 B 5 0 30012 86 0 35125 B 0 36453 B 8 0 34727 B 9 030682 B 10 0 25071 B 11 Innovation variance 0 0055 irregular Non stationary AR 1 Stationary AR 1 MA 1 Innovation variance 0 6779 Next section includes several tests First of all variances of the component innovations are displayed variance of the component innovation Component theoretical variances of the stationary transformation of the estimated components Estimator empirical variances of the stationary transformation of the estimated components Estimate 2 SEATS identifies the components assuming that except from irregular they are clean of noise It implies that the variance of irregular is maximized on the contrary the trend cycle and seasonal component are Stable as possible The table compares the variance of the stationary transformati
14. g n n l 7A n Where S is the sum of the ranks of the observations 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 4 4 3 Test for the presence of seasonality assuming stability The test statistics and testing hypothesis are the same as for Friedman stable seasonality test described in 4 4 1 Annex 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 4 4 4 Evaluative 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 t e Additive ST X b m e Where m refers to the monthly or quarterly effect for 7 th period 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 DEMETRA User Manual doc 135 DEMETRA User Manual N gt xX ij X e the total sum of squares i l s Me II _ l N S ky X X the inter month inter quarter respectively sum of squ
15. the total sum of squares 1 k _ S So X X a variance of the averages due to seasonality n k S gt X X the residual sum of squares j l i l Explanation of the test and symbols is included in Annex The test statistics is calculated as Si F F k Ln k R n k where k 1 and n k are degrees of freedom 20 http support sas com onlinedoc 913 DEMETRA User Manual doc 89 DEMETRA User Manual The example is shown below Test for the prese ____ Sum of squares degrees of freedom Mean square rA To oas Value 105 6725 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 Evolutive ality test SCSCSC di Sumo squares Degrees of freedon Mean square Benween veer Between years 0 021 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 Combined test identifiable seasonality present Residual se test No evidence of re
16. 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 gt Floating Tabbed gives access to that functionality 5 Closed panels can be re opened through the main menu commands Workspace gt View gt 6 See 3 5 for detailed description of this functionality DEMETRA User Manual doc 11 DEMETRA User Manual Time series can be dragged and dropped between windows next section presents how to do it This function is omnipresent in Demetrat It is the usual way to move information between different components The objects that can be moved time series collections of time series can take different forms nodes in trees labels in lists headers in tables lines in charts 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 which indicates an acceptable drop zone Time series from Excel can easily be integrated in Demetra The users can create and import their own data sets The series must be formatted in Excel as follows e True dates in the first copied column e Titles of the series in the corresponding cell of the first column e Empty top left cell A1 e Empty cells in the data zone correspond to missing values except at the beginning and at the end of the series That format corres
17. yl Provided that the regression variables are independent it is possible to find an orthogonal matrix Q so that R Q X where R is upper triangular That matrix is built by means of Householder transformations reflections We have now to minimize 2 2x2 Oy oP Qy RB all2 I bI 2 where DEMETRA User Manual doc 128 DEMETRA User Manual QY o x1 a and QY 1 b It is trivially done by setting p R a In that case RP a 0 The residuals obtained by that procedure are then b 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 3 Specifications RSAO Level Airline model RSA1 Log level outliers detection Airline model TramoSeats one Log level working days Easter outliers detection Airline 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
18. 1 Full residuals 0 05 0 0 05 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 0004 0022 0035 O019 OO 0007 0006 0024 0 020 1992 0004 0018 0002 O007 OfO16 Of14 0005 0030 0001 0 005 0 008 0 024 1993 0040 0 020 0028 0024 0008 0 011 0 006 0002 0008 0008 0 020 0 029 1994 0014 0012 0 016 0 028 0031 0 006 0006 0005 0007 0012 0 004 0 019 1995 0 028 0 011 0012 O08 0002 0 005 0007 0006 0073 O01 0009 0016 1996 0009 0005 0015 0002 0003 0006 00144 0029 0011 0 010 0009 0 015 1997 0 007 0009 0010 0037 0002 0014 0012 0011 0 016 0031 0 029 0 015 1998 0 017 0 023 0022 0004 0015 08005 0028 0024 0015 0011 0004 0 007 1999 0013 0005 0000 0 028 0019 0006 0000 0005 0002 0036 0012 0 016 2000 0 006 0 022 0006 0000 0012 0024 0001 0027 0007 0 029 0018 0 042 2001 0 023 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 Summary Statistics are presented in the following tables 1 No of the residuals oo e SUS Norma 2 in ndence of the residuals Coo o Ljung Box 24 05164 Box Pierce 24 05781 O Ljung Box on seasonality 3 04087 sid Box Pierce on seasonality 3 O2 OoOO O 3 Randomness of the residuals Liung Box on squared residuals 24 B
19. 1000 The diagnostics output window provides some purely descriptive features to analyze the stability of some part 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 judging about the stability of the model parameters On the picture be 0 02 0 015 0 01 0 005 0 005 0 01 0 015 0 02 0 025 low the results of model stability diagnostic are shown Monday Tuesday Wednesday Thursday Friday Saturday Sunday DEMETRA User Manual doc 98 DEMETRA User Manual 0 2 0 3 e o o Ma o y5 0 4 ao o o o e 0 5 e 0 6 e o 0 7 z 0 8 Phi 1 Phil2 BTheta 1 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 Oo Seasonality tests o Spectral analysis DEMETRA User Manual doc 99 DEM
20. 101 24 Q without M2 4 3 2 1 4 Diagnostics The Diagnostic panel contains detailed information on the seasonal adjustment process summary 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 g without m2 Good 0 455 DEMETRA User Manual doc 83 DEMETRA User Manual e Basic checks This section offers a set of quality diagnostic o Definition This test is inspecting some basic relationships between different components of the time series The following components are defined tae _ __ ote _f Original series esses yc _f Interpolated series Y with missing values relaced by their estimates T tif Trend without regression effects _ A i Irregular without regression effects C TOR itd f Trading days effects SSS MHE mb _f Moving holidays effects C effects RMDE Ramadaneffects SS OMHE _ Other moving holidays effects OTOT Bit liers effect 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
21. 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 The detailed tables list can be found in the Annex Quality measures DEMETRA User Manual doc 81 DEMETRA User Manual 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 The M statistics are used to judge the quality of seasonal adjustment 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 preliminary estimate of the seasonally adjusted series as if this ratio is too large it is difficult to separate the two components Statistic M4 tests the randomness of irregular component Statistic M5 statistic is used to compare the significance of changes in trend with that in irregular Statistic M6 checks the I S irregular seasonal component ratio as if annual changes in the irregular component are too small in relation to the annual changes in the seasonal component
22. 1994 120 7637 3 1 1994 120 8408 4 1 1994 120 6459 5 1 1994 120 5538 lt 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 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 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 For the additive decomposition absolute revisions are used otherwise relative differences are considered The largest differences are displayed in red They correspond to values that are larger in absolute term than 2 times the root mean squared error of the absolute or relative revisions DEMETRA User Manual doc 94 DEMETRA User Manual Relative differences mean 0 0679 msze 71 5667 a E RO E E E CC EE Febuary A E a E a e O March a EE A ET a E S sd se C a E a E ao A my om o fees o oeo ors Sa E E E a a E E E A E August E a E e E e S September 260 faoss foss e otor foo O ose fosa fosa O OOOO O Movember oz oon fias ose ooo December oss ose lt josz joss Sliding spans It is expected that seasonally adjusted data
23. Automatic modelline Trading days Length of period Holidays Holidays Specific holidays B Example user defined trading days Specifications x12Doc 1 AICC Difference El Trading days Calendar effecta Type Regression Pretest Anma modelling A Details Automatic modelling ltem E stimatior Decomposition 11 User variables E Example Easter effect Specifications X17Do0c 1 o gt Basic AICC Difference F Transformation El Trading days Calendar effects Type 2 Regression Pretest E Arma modelling Details Pretest statistics for w 1 6 15 Calendar True Td Hone lt to sel UserDetined True 3 tems td tda wth Predetined True Pretest the significance of the easter regression vanal DEMETRA User Manual doc 46 DEMETRA User Manual 4 1 3 2 E _ Comments e n spec Pre specified regression variables User defined outliers used where prior outliers knowledge suggest such effects at known time points e aoyyyy pp additive point outlier which occurred in a given date AO Isyyyy pp regression variable for a constant level shift beginning on the given date LS tcyyyy pp regression variable for a temporary level change beginning on the given date TC Seasonal outliers are not supported Pre specified outliers are simple forms of intervention variables Ramps regression variables Ramp effect which begins
24. B5 Seasonal Component Table B6 Seasonally Adjusted Series Table B7 Trend Cycle Table B8 Unmodified Seasonal Irregular Component Table B9 Replacement Values for Extreme SI Values Table B10 Seasonal Component Table B11 Seasonally Adjusted Series Table B13 Irregular Component Table B17 Preliminary Weights for the Irregular DEMETRA User Manual doc 138 DEMETRA User Manual 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 SI Table C5 Seasonal Component Table C6 Seasonally Adjusted Series Table C7 Trend Cycle Table C9 SI Component Table C10 Seasonal Component 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 SI Table D5 Seasonal Component Table D6 Seasonally Adjusted Series Table D7 Trend Cycle Table D8 Unmodified SI Component Table D9 Replacement Values for Extreme SI Values Table D10 Final Seasonal Factors Table D10A Forecast of Final Seasonal Factors Table D11 Final Seasonally Adjusted Series DEMETRA User Manual doc 139 DEMETRA User Manual Table D11A Final Seasonally Adjusted Series with Revised Annual Totals
25. For a detailed description of the X12 specifications you should refer to the Demetra_Spec docx document 3 4 TramoSeats Doc This item is added to the application s menu when seasonal adjustment using TramoSeats method was previously done and after that it was activated by the user This item offers the similar options set as the X12Doc TramoSeatsDoc 1 Specification Current specification Copy b Paste Lock Add to workspace 3 5 Window menu Window menu offers the following functions e Floating show additional information 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 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 DEMETRA User Manual doc 38 DEMETRA User Manual Tile vertically Tile horizontally 5 ri es ay zx g Tramosepts Dot Skin ning 1 S4Processing 1 TramoSeatsDoc 2 E Preq 40000 35000 30000 tick indicates which window is active now g 20000 As an example the following chart presents t
26. Tsw usce Name Type Freq Start End Description Var_1 Dynamic 12 G ai Variables sds 4 My varables 4 7 i Var 5 a Var l s a Var3 1000000000 es Vrd ae and drop a variable 01 1950 01 1970 01 1990 01 20 01 1960 01 1980 01 2000 The 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 showed 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 Because of that it is a convenient solution for creating user defined variables 3 2 Tools menu Tools menu is divided into tree parts DEMETRA User Manual doc 25 DEMETRA User Manual e Container tools for displaying data e Tool Window charts and data transformation e Options different windows diagnostic and output options that can be set by user Tools Container a ToolWindow Options The contents of tool windows are automatically updated when e Anew series is selected through a double click in the browsers panel or when a series is dropped in the left zone of the X12 window e The specification is changed by means of the specification dialog box or when another specification coming from the workspace is dropped in the left zone of the X12 window Many other combinations are of course possible Be advised that the current implementation is not able to dete
27. W R Otto M C Chen B C 1998 3 X 11 program was introduced in 1965 See SHISHKIN J YOUNG A H and MUSGRAVE J C 1967 DEMETRA User Manual doc 6 DEMETRA User Manual overview of the software capabilities and of its main functionalities Moreover step by step descriptions how to solve some very basic tasks are included It will give the possibility to reproduce results with user s own data The guide shows the typical path to follow and illustrates the user friendliness of the application It is expected that the readers have already acquired background knowledge about concept of seasonal adjustment and are 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 restricted with regard to their original implementations For this reason there are some differences between original programs and programs implemented in Demetrat The aim was to develop the software which enables the comparison of the result from TramoSeats and X 12 ARIMA For this reason revision history and sliding spans analysis are available in Demetra both for TramoSeats and X 12 ARIMA On the contrary some functionalities implemented in original programs are missing in Demetra e g using X 12 ARIMA under Demetra it is not possible to cho
28. during session 7281 1 DEBUG Demetra WorkspaceControl null WorkspaceControl initialized a 51421 1 DEBUG TSPFroviders Eecel EecelVersion Strategies null Ecel Version Strategy Excel 2007 disabled 62233 1 ERROR TS Toolkit SeasonalAdjustment TramoSeats 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 TSToolkit SeasonalAdjustment TramoSeats Monitor null IMPORTS CIF Series LENGTH should not be gt 600 117998 1 ERROR TSToolkit SeasonalAdiustment Tramo Seats Monitor null IMPORTS CIF1 Series LENGTH should not be gt 600 x The user can also display messages which belong to a chosen category like ERROR EMERGENCY see the picture below E ERROR a SEVERE CRITICAL ALERT FATAL EMERGENCY OFF 2 6 Results panel The black area 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 Those windows will overlap each other with the foremost window being in focus or active Only the active window has a darkened titlebar The example below shows the typical view of this panel The right part of the panel presents navigation tree while on the left th
29. file named by the system workspace_ number that can 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 e Recent Workspaces opens workspace recently saved by user e Exit closes an open project Edit Calendars Import User variables Recent Workspaces P Exit DEMETRA User Manual doc 20 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 the different number of the week 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 of the extra day inserted into February every four years These differences cause regular effects in some series
30. 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 INDUSTRIAL PRODUCTION 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 schema Excel TSW USCB Text and ODBC The installation procedure has copied several files in different formats in the subfolders of My Documents Data The way how to open Excel workbooks is presented below The procedure is similar for the other providers Click on the Excel tab of the browsers panel Click on the left button see below Choose an Excel workbook for instance insee xlsx in the folder My Documents Data Excel tt Demetra Prototype IV Workspace Seasonal adjustment Tools Window Help Browsers AD r cessing 1 Modified 12 1899 01 1900 DEMETRA User Manual doc 13 DEMETRA User Manual 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 whole workbook and in eac
31. orthogonal components The table below contains the correlations between the stationary transformations of the estimators and of the estimates DEMETRA User Manual doc 103 DEMETRA User Manual actually calculated by SEATS The last column PValue displays the results of the test for no correlations between components In the example below PValues are green which indicates that all correlations are negligible Cross correlation OOOO o Eor OE Vale rend seasonal l frendiseasonal Joma 00794 07135 irendirregular seasonalirregular moss noos Additional information presented by Demetra is set of stochastic series seasonally adjusted series trend seasonal component irregular component trend forecast seasonal component forecast and Wiener Kolmogorow analysis Wiener Kolmogorow analysis concentrates on2 o Components spectrum ACGF o Final estimators spectrum square gain function WK filters ACFG PsiE weights o Preliminary estimators Frequency response square gain function phase effect WK filter ACFG o Revision analysis total error revision error Revision analysis compares the variance of the different estimation errors for the historical estimators of the trend cycle seasonally adjusted series seasonal and irregular The graph shows the duration of the revision period i e how many periods it takes for a new observation to no longer significantly affect the estimate 2 gt Wiener Kolmogorow analy
32. 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 9 According to G MEZ 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 DEMETRA User Manual doc 50 DEMETRA User Manual Calendar effects balanced Controls whether the automatic model procedure will have a preference for balanced models 4 1 3 4 Arima Options included in this section are active only if IsEnabled parameter from Automatic modeling section is set to false Comments Individual spec Argument Mean regression variables It is considered that the mean is part of the Arima model it highly depends on the chosen model Only Box Jenkins SARIMA models p d BQ q bp bd bq is considered theta btheta The coefficients are defined using the phi bphi convention used in TramoSeats It means that they are the opposite of the coefficients used in X12 X12 specifications Basic Mean Transform
33. the aictest parts of the regression spec The specified length of the Easter effect is used When he 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 regression aictest Pretest the significance of the Easter regression variables using AICC statistics regression easter w Duration of the Easter effect w parameter of the easter variable The parameter is active if the aictest None The current version of Demetra doesn t allow the use of stock trading days Regression variables for the handling of Labor Day and of Thanksgiving are not handled Example predefined trading days Specifications X12Doc l AICC Difference 0 Transformation E Trading days Calendar effects Type Predetined Regression Pretest True E Arima modelling E Details Outliers detection Trading days TdNoLpYear E stimation Length of period Hone F Decomposition 11 El Easter effect In Use ls enabled Type Type of regression varables DEMETRA User Manual doc 45 DEMETRA User Manual Example calendar trading days Specifications X12Doc 1 AICC Difference Transtormation El Trading days Calendar effects Type Regression Pretest Fl Anima modelling El Details
34. the 3X5 seasonal filter used for 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 used in the model Statistic M7 is the combined test for the presence of identifiable seasonality The test compares the relative contribution of stable and moving seasonality Statistics M8 to M11 measures 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 Q without M2 also called Q2 is the Q without the M2 statistics Q 10M14 11M24 10M3 8M4 4 11M5 10M6 18M7 7M84 7M9 4M104 4M11 100 Otherwise its weight in q is zero 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 calculated as ee NO a Daa ee a A A 100 The model has a satisfactory quality if Q statistic is less than 1 Results of the test Treshold 1 21 16 For the definition of the M statistics refer to Ladiray D and Quenneville B 1999 DEMETRA User Manual doc 82 DEMETRA User Manual Summary and Quality measures Final fiters Trend filter 9 term Henderson moving average Seasonal fiter 3 x 5 moving average Doo e Sn e e Total oes Jers Jan Sd
35. the average of the defined diagnostics Bad 1 Uncertain 2 Good 3 is lt 1 5 Uncertain No error no severe diagnostics the average of the defined diagnostics CO Bad 1 Uncertain 2 Good 3 is in 1 5 2 5 Good No error no severe diagnostics the average of the defined diagnostics ae Bad 1 Uncertain 2 Good 3 is 2 2 5 According to the table errors 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 13 The model also contain a flag Accepted which simply means that the statistician decided to accept the results no matter what are the different diagnostics DEMETRA User Manual doc 71 DEMETRA User Manual 4 3 2 1 X 12 ARIMA 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 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 DEMETRA User Manual doc 72 DEMETRA User Manual 4 3 2 1 1 Main results This section includes basic information about pre processing and the quality of
36. the multiprocessing SAProcessing xx default he can also add the multi processing to his workspace for future re use and he can decide if the execution is automatically started the default when the wizard is closed It should be mentioned that he can go back to the first step of the wizard at any time if he 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 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 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 please 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 DEMETRA User Manual doc 110 DEMETRA User Manual EE SAProcessing 1 i iol x Series Method Processing Priority Quality Unemployment TS RSA3 Concurent Valid I S
37. version Detailed aspects of saving the results in external files are discussed in the next section 4 6 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 appropriate box in left hand part of the Output window The settings which are displayed in the second part of the window come from Tool gt Options menu All changes in those settings should be done in the Tool gt Options menu If the user changes the settings e g output s folder in the SAProcessingXXxX gt Generate output window or TSProcessingXXX gt Generate output it will not have any effect on the output s content DEMETRA User Manual doc 120 DEMETRA User Manual SAProcessing 2 Update reports CADocguments and Scttings st Sag Edit gt E ye calendar comected series False Priority I A False Tiue True ai F type e Add to workspace neri ati True Jnitial order these settings must be specified in the tool gt options menu For multi processing that don t belong to a workspace output files name is def
38. 1 1 1 25 00 0 1 0 0 1 1 1 25 00 0 1 0 1 0 1 1 25 00 Sa 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 Easter corrections 0 0 00 Last section Matrix view panel provides information similar to the matrix output of TSW TramoSeats for Windows 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 theirs 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 DEMETRA User Manual doc 112 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 Le a E a m fs gt of G i The
39. 68 100923 101 171 101 426 101 594 101 559 10 2002 101 566 101 632 1664 101 847 102 185 102 351 102 292 102 094 101 89 101 774 101 757 10 2003 101 359 101 1 100 82 100 465 100 151 99 9691 99 9146 99 907 99 8583 99 7808 99 7042 99 2004 99 9209 100 02 ann 11e arn ann ore Ann Wa ara ann 490 ann cnn ann cr ann cenn anrc 10 2005 100 517 100 359 L akdkikk 15 x 2006 100 061 100 271 2007 101 707 101 486 2008 99 8345 99 6718 2009 101 887 102 244 jo aw 90 01 1990 01 1992 01 1994 01 1996 When a container is active its name is added to the menu toolbar 01 1998 01 2000 01 2002 01 2006 01 2008 01 2004 01 2010 The chart or growth chart is automatically rescaled after adding new series Also new item Chart or Growth Chart respectively is added to menu toolbar Workspace Seasonal adjustment Chart Tools Window Help 2500000000 2000000000 1500000000 1000000000 500000000 0 J rll Skea Lit ela ee ae ell 01 1970 07 1975 01 1980 01 A nj gi i jii Se j af Ary W l Ti T t 1985 01 1990 01 1995 01 2000 01 2005 01 2010 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 DEMETRA User Manual doc 28 DEMETRA User Manual 3000000000 EXPORTS EXPORTS FOB IMPORTS CIF IMPORTS Cll 2500000000 IMPORTS CIF i 2000000000 1500000000 7000000000
40. 91 Y5 0 17263 7 672631 6566 0 731528 11737 07 01 05 1991 9 0 32509 8 225092 i24 0 699145 12476 14 8 01 06 1991 6 6 0 166 6 755001 11795 0 946077 12440 965 Ea 01 07 1991 9 6 0 155109 9 444691 10356 0 880188 11767 94 10 01 08 1991 10 1 0 170372 9 929626 6616 0 509065 10651 8 11 01 09 1991 10 7 0 09329 10 60671 10104 0 624546 12253 98 42 01 10 1991 11 1 0 08194 11 16194 10712 0 991832 10800 21 13 01 11 1991 11 2 0 09951 11 49951 12695 1 136479 11170 46 fa 01 17 1991 0 07322 11 afi 30960 7 642777 11 61 68 bi Jal f ODBC 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 j Save original series Save calendar effects Save sa seres Save seasonal component Save trend Save iregular component Save model CSV Using the csv format it is possible to generate for multi processing documents a large number of time series generated by the models Each file will contain for all the series of the processing 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 eac
41. Demetrat User Manual E eurostat I NationalBc nk CF BELGILAN Tramoseats Furcsyste Sylwia Grudkowska National Bank of Poland March 2011 DEMETRA User Manual Acknowledgements would like to thank all the members of the Steering Group on seasonal adjustment for their useful comments and helpful suggestions on various drafts of this document Thanks are due to Dominique Ladiray INSEE Jean Palate National Bank of Belgium Anna Ciammola ISTAT Faiz Alsuhail Statistics Finland Dario Buono EUROSTAT Joerg Meier Bundesbank Michael Richter Bundesbank and Kevin Moore ONS for their valuable support and contributions to the preparation this manual DEMETRA User Manual doc 2 DEMETRA User Manual Contents COS BS ecg cecee ch Serene neste T niene onc aan sete nee hese Bade E E E see Mecsas os nese adores sc aantese 3 TGC Cl OW ca sarc sncesucasenssinesancenatea A E E E EE PEO PE A E E E A E 6 TELCO aO a a E E E E E T 8 BL ADU DEME t sssauccacedcanisnttcennmerenavex si linia tanaiied ekeson td oraanubondeoscanianantcanrcherss avaenoueiivertonnananar 8 1 2 Uninstall previous version Of Demetra t ccccccceeccceescccececeeecsceeueceeeneeeeeeseseueceetceteneseeeueeeeens 9 TO VAS CANINE DENE a accacosctoe sane cone conan E E AS 9 1 4 RUNNING Deme a ennea 9 LS Cee DEMNE erer e E E A ees 10 2 Main application s WINGOWS cccccccsseccccesecccesececcesecccceneccceceesecessueceseueeceesauecessuaecess
42. Differences across spans 35 00 30 00 06 25 00 02 si 15 00 0 4 10 00 5 00 02 0 00 0 25 3 a5 If the result of the Sliding spans analysis reveals many unstable estimates it can support an idea of changing the model s specification The example of such situation is presented below Because of the large share of moving seasonality the test for presence of identifiable seasonality failed 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 a E CY SY Sabes fer o fee o po o ma o Kruskal Wallis ss fsz o Jsa o r Movngsess Ja a fe o a CS dentinable sess mo pmo ho o Means of seasonal factors S E E E E February Jasna asos oarsas asena maen ase o ezia araea aosa orl E e E T E C e T a a E E oy mos an m aO O mog ossa ___ 1064 05 faroa aerose Septem Janasa feeasee manr mar October e9255 oraa mon ponr November Jaso asio rozz anaes DEMETRA User Manual doc 97 Model stability DEMETRA User Manual 2000 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
43. ETRA User Manual o Revisions history o Sliding spans o Model stability Detailed description of the seasonal adjustment outcomes is presented below Because the majority of features are very similar to the X 12 ARIMA the appropriate drawings are omitted The user can find them in Seasonal adjustment results for X 12 ARIMA In this section only those issues specific for TramoSeats will be discussed in details 4 3 2 2 1 Main results Basic information about seasonal adjustment and the quality of the outcomes are presented in the following way trend Innovation variance 0 0966 seasonal Innovation variance 0 0372 irregular Innovation variance 0 2663 summary Good basic checks definition Good 0 000 annual totals Good 0 004 spectral seas peaks Bad spectral td peaks Good reganma residuals normality Uncertain 0 036 independence Good 0 290 spectral td peaks Good 0 176 spectral seas peaks Bad 0 006 on sa Good 1 000 on sa last 3 years Good 0 983 on irregular Good 0 066 outliers number of outliers Good 0 010 seats seas Variance Good 0 394 irregular variance Good 0 539 seaslirr cross correlation Good 0 434 Additional information is available in three subsections Charts Table and S I ratio DEMETRA User Manual doc 100 DEMETRA User Manual In Charts section the user will find o the original series with forecasts o the final seasonally adjusted series o the fi
44. Exclude Delete Clone Active Open opens the specification window with information about 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 specification chosen Time series will be seasonally adjusted using this specification E Workspace_1 El Single processing Tramo Seats X12 das Multiprocessing Specifications TramoSeats Open RS RS Delete RS Clone RS 7 Active Trae 4 E X12 X11 RSA1 RSA2c RSA3 merase In a similar way the user can add new specification in single processing and multi processing sections This can be achieved by right clicking on the seasonal adjustment method Workspace_1 ot ro Sir gle processir 1g Tramo Seats Add New Add Existing Exclude All RSAO RSA1 RSA2 RSA3 RSA4 RSA5 TramoSeatsSpec 1 X12 X11 RSA1 RSA2c mean DEMETRA User Manual doc 17 DEMETRA User Manual 2 5 Log Log window keeps information about all bugs warnings and other events that took place
45. I CAPITAL CITY TS RS5A5 Concurrent Valid l x CRUDE PETROLEUM F TS RSA5 Concurrent Valid x definition Good 0 000 EXPORTS FOB 12 R5A3 Concurent Valid x annual totals Good 0 000 x IMPORTS CIF1 12 RSA3 Concurrent Valid IMPORTS CIF1 a GENER ommamene HE TS RSA3 Unemployment Apply Restore Save E H Main results H Pre processing Tramo hood 0 234 I Decomposition Seats ice Good 0 262 ie peaks Uncertain 0 030 H Diagnostics as peaks Uncertain 0 013 asonali d 1 000 3 years Good 1 000 Good 0 457 ls enable True trend Innovation variance 0 2291 Outliers d Weea2onal Innovation variance 0 0976 Option AO_TC_LS Wirreguiar Innovation variance 0 0292 puthers Good 0 026 Defaut c True Critical ve 3 5 EML estir False Erte 07 Unemployment SA series 01 2000 01 2010 eee pe 0 01 199501 199601 199701 199801 1999 01 200001 200101 200201 200301 2004 01 200501 200601 200701 200801 200901 201001 2011 New processing 7items 1 1 0 0 1 1 ao 2 tc 1 Is 2 If the result is acceptable the user can save it to the multi processing window using Save button The multi processing contains now the adjusted specification for that series Otherwise the user can come back to the previous settings using Restore button It is not necessary to close the details window to get information on another series that window is updated by a simp
46. MA 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 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 This 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 1 TRAMO Time Series Regression with ARIMA Noise Missing Observations and Outliers and SEATS Signal Extraction in ARIMA Time Series are programs supported by Bank of Spain for more details see G mez V and Maravall A 2001 Caporello G and A Maravall 2004 2 X 12 ARIMA is supported by the US Bureau of Census for more details see Findley D F Monsell B C Bell
47. Manual 1 15 1 1 0 9 Jan Feb Mar Apr a9 1990 1995 2000 2005 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 see below 20000 15000 10000 y 5000 5000 10000 15000 20000 2000 1980 1985 1990 1995 2000 2005 2010 25000 T I T T S I ratio chart is a useful diagnostic tool This chart is helpful for detecting the presence of seasonal breaks These would show up as an abrupt changes to the level of the S I ratios A seasonal break could distort the estimation of the seasonal component and because of that it should be appropriately modeled Sl ratio chart also reveals the periods with more statistical variability than other periods If the SI ratios 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 15 See Guide To Seasonal Adjustment 2007 DEMETRA User Manual doc 75 DEMETRA User Manual Changes in seasonality over time are acceptable unless there is a noticeable change from below to above the overall mean The overall mean is equal to 1 in case of additive model and 0 in case of multiplicative model The problem is illustrated with the chart below The S I ratios for majo
48. OUR DUNS wir dicdata sclera hae ee a a 34 DO 1A DOC n sea ca scat Gue feu eau a O eases ieeeseonieeeeieeto 37 3A TRAMO Seats DOC sanar E awenan maspodanen manus conwasae taapenuaasovecdiacuneenenqauwanuienaneeueens 38 5 WVIGOW WON Usexeas tem orset fe csant ts a cats coc aus te canc ee eecudanacageatieaence a a 38 rales errs 18 as Brel 8 U TME NE sega a mel res nme eee teeta PERE ee oR or Rea ee eer eee eee ete 41 rad Dat WAR of X el hers nd g pene eee PI eI ene Cre aR PRE sk eee nee eee 42 4k Generaldeschip Onesia A A E TAN 42 AL BIS anaa aa aa eet a a hamedathsandsekeaagats 42 A S TaN Orna UO ee A E ewes 43 Ake MC SIEGE I LOCls areena a aa a a 43 AV 32 REE VSSSION iaa a a ae a a a e eietivl os iaeealocbed Meieietias 47 A loa AULOMALIC modeline vrasin AEN NOAA 50 Ak S ARA aa a a N a beasties 51 Al S Outer CCL CCUI OM artis sate ahias ra N T 52 Ak S O ESMA UO Mnara a a e E N NE a E teat ias 53 4l or CCOMMIOS Hon A L era a T ue naasaaeeas 54 42 TVAMOSC dat S lt SDECITICALIONS serii E E Hatin dene Acbileoasieuteden 55 42 1 General descripPUO Misdevecetedeveecessd stacy cactcvensasauatelosd econedtueastddaseeanoedeessaustant ouseeooeasautacsde tees 55 ral a NOMO ene nn cr EE ee 55 4221 Calendar effett Snoen a a a a 56 4222 RECESSION eaa castes eeduanudensuaseannleas 59 42 2 5 Automatic modeling ducccdnci ee Meas i tice dei dai deet ees ee aehdeds 61 A2 ZA ANNA cciataieaahcoulasedacuk catanicessie pea kiatahone pean nsansaaisaut
49. SCIF Source XCLPRVDR E Statistics Time span 1 1957 to 6 2009 Number of observations 630 Number of missing values 0 0 01 1950 01 1970 1 199 01 1960 01 1980 01 2000 Then the methods could be selected DEMETRA User Manual doc 68 DEMETRA User Manual Single analysis Wizard Finishing 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 Single analysis Wizard DEMETRA User Manual doc 69 DEMETRA User Manual Obviously the user can define the new specification 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 4 3 2 Seasonal adjustment results single processing Specifications correspond to the terminology used in TramoSeats12 and are described in Annex Once the active specification is chosen the user just has to make a double click on the series in the browsers panel that he wants to adjust The processing is immediately initiated with the selected specification and the chosen series Demetra Prototype IV E O x Workspace Seasonal adjustment TramoSeatsDoc 2 Tools Window Help Browsers n X Workspace 4 X Xmi Excel Tsw usce FS ae Eg Or d w
50. TRA User Manual doc 29 DEMETRA User Manual 101x 12 00 _ Unemployment 10 00 8 00 6 00 4 00 2 00 Copy Export Copy growth data Print gt Remove 2 00 Legend Copy all Kind gt Copy all growth data ii tt a Remove all 6 00 Paste m a aa aan a 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 Tool window offers the following options TS Properties Chart Growth Chart Seasonal Chart Spectral Analysis and Differencing First three of the above have been described in previous sections Others are characterised below 3 2 2 1 Seasonal chart Seasonal chart presents the final estimation of the seasonal irregular component and final seasonal factors for each of the period in time series months or quarters To calculate them Demetra uses the active specification the one which is marked in the Workspace menu E F Workspace _7 o odia gt Tramo Seats E E Kiz x 100 wa a a RSA3 of cnt P pel J m yf RSASe 50 Jan Mar May Jul Sep Nov AlzSpec 1 Feb Apr Jun Aug Oct Dec 2 Calendars 2 Default User defined variables The curves visible on the chart represent the final seasonal factors and the straight line represents the average for these values in each period DEMETRA User Manual doc 30 DEMETRA User Manual 3 2 2 2 Spectral analysis Demetra offers tw
51. 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 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 6 Visual spectral analysis The autoregressive spectrum estimator is defined as follows 8 s A 10l0g 04 _ _ pe 1 9 9 gre j l 20 where 33 Definition taken from X 12 ARIMA Reference Manual p 55 http www census gov srd www x12a DEMETRA User Manual doc 140 DEMETRA User Manual A frequency 0 lt 2 lt 0 5 A O m the sample variance of the residuals A coefficients from regression x x on x x 1S j lt m A A Criterion of visual significance is based onthe range s s of the s A values where A m s max s A A s min s A The value is considered to be visually significant if s A at a trading day or seasonal frequency A other than the seasonal frequency Ae 0 5 must be above the media
52. 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 Espa a 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 1993 Stochastic linear trends Journal of Econometrics 56 1993 5 37 MARAVALL A 2008 Notes On Programs TRAMO and SEATS TRAMO par http www bde es webbde es secciones servicio software tramo Part_Il_Tramo pdf MARAVALL A 2006 An application of the TRAMO SEATS automatic procedure direct versus indirect adjustment Computational Statistics amp Data Analysis 50
53. able and then revision history can be used for choosing the better model in terms of revisions More detailed description is available in Annex 112 110 108 106 l o 104 102 rA fs el A a gg 96 94 06 2005 11 2005 04 2006 09 2006 02 2007 07 2007 12 2007 05 2008 10 2006 03 2009 08 2009 If the user clicks on a blue circle which represents the initial estimation for period an auxiliary window will appear The figure shows the successive estimations computed on f tosta fos gt r of the considered series for the period From this figure the user can evaluate how the seasonally adjusted observations were changing from initial to final estimation The analogous graph is available for trend analysis DEMETRA User Manual doc 92 DEMETRA User Manual 112 110 106 104 102 100 98 96 94 06 2005 11 2005 04 2006 09 08 2009 04 2006 02 2007 12 2007 10 2008 08 2009 09 2006 07 2007 05 2006 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 right bottom 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 the expense of the speed of t
54. able values predefined e LeapYear include a contrast type or calendar variable for leap year type LengthofPeriod include length of month or length of quarter as a regression variable Can be disabled when the adjust option is used in the transformation specification or with some trading days options Holidays When the user chooses the calendar type calendar type for the trading days he must specify the corresponding holidays It should be noted that such a holiday must have been previously defined see 3 1 1 Items regression user When the user chooses the userdefined UserDefined usertype type for the trading days he must specify the type td corresponding variables It should be noted that such variables must have been previously defined see 3 1 2 Easter regression variables The option enables the user to estimate the IsEnabled and or Easter effect in tree different ways aictest The user can choose between tree pre test options e Add e Remove DEMETRA User Manual doc 44 DEMETRA User Manual Comments a e spec 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 regression spec An automatic identification of the Easter length between 1 8 and 15 days is executed When he chooses the Remove easter is added in the variables an in
55. ad time series 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 bookmark Xml Excel TSW usce BT oaa r5w All seres fe Monetary Aggregate ALP Spain CPI Spain T EXPORTS JAPAN GNP USA IMPORTS DEMETRA User Manual doc 15 DEMETRA User Manual 2 3 TS Properties TS Properties window contraction from Time Series Properties can be used for examination the characteristics of individual series This panel is strictly connected with the 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 launched by single clicking on the time series name in the 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 Metadata Statistics Time span 1 1995to 11 2010 Number of observations 191 Number of missing values 0 Min 1352 3 Max 3344 2 Average 2411 411 Median 2445 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 Wor
56. ameter was calculated The P value indicates that the regressor is significant ARIMA model 0 1 0 0 1 1 Parameter Value Sid enor P yalue ATh 1 0 3376 0 0882 0 0002 Using RSA5c specification trading days effect has been detected It can be noticed from the table below 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 Calendar effects Trading days Parameter Value Std error 0 632428 040 06931 Sunday derived 0 659838 Join F Test on trading days F 4 1350 P Value 0 0010 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 DEMETRA User Manual doc 77 DEMETRA User Manual Easter Parameter Value Sid enor T Stat P value 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 location parameter s value and significance Detected outliers Parameter St
57. and ends on a given dates rpyyyy pp zzzz qq All dates of the ramps must occur within the time series Ramps can overlap other rams additive and level shifts outliers Intervention regression variables No corresponding X12 arguments The variables intervention variables are defined as in Tramo Following their 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 This option enables the user to define four types of intervention variables e Dummy variables e Any possible sequence of ones and Zeros l of any sequence of ones 1 B and zeros 0 lt 0 Delta lt 1 l _ 4 of any sequence of ones 1 0 B and zeros 0 lt 0 DeltaS lt 1 8 User defined regression user The user defined variables effect can be variables usertype assigned to the trend irregular of holiday or can exist as an additional component option None For those variables the user can specify lags 8 See BOX G E P and TIAO G C 1975 DEMETRA User Manual doc 47 DEMETRA User Manual Example Pre specified outliers Example Ramps ha j 1 Ra mpProperties DEMETRA User Manual doc 48 DEMETRA User Manual Example Intervention variables p Basi Pre specified 2 items i 0 tc 1 2000 a 1 I
58. are stable which means that removing or adding data points at either end of the series does not change the SA results very much Sliding spans analysis is useful in case of seasonal brakes large number of outliers and fast moving seasonality The sliding spans analysis checks the stability of SA A span is a range of data between two dates Sliding spans are series of two three or four depending on the length of the original time series seasonal moving averages used and series frequency overlapping spans The sliding spans analysis stands for the comparison of the correlated seasonal adjustments of a given observation obtained by applying the adjustment procedure to a sequence of three or four overlapping spans of data all of which contain this observation The procedure of withdrawing spans from time series is described in FINDLEY D MONSELL B C SHULMAN H B and PUGH M G 1990 The program sets up 4 spans of 8 years separated by 1 year 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 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 The summary of Sliding spans analysis is presented below It contains information about spans results of the seasonality tests and means of seasonal factors for each mo
59. ares i l N S k X je X e the inter year sum of squares i l N WN z S X X X ie Xe j X the residual sum of squares i l i l 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 DC 1 which follows a F distribution with k 1 and n k degrees of freedom 4 4 5 Test for presence of identifiable seasonality This test combines the F statistic values of parametric test for stable seasonality and for the moving seasonality 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 4 4 6 Combined seasonality test This test combines the Kruskal Wallis test 4 4 2 along with test for the presence of seasonality assuming stability 4 4 3 evaluative seasonality test 4 4 4 and test for presence of identifiable seasonality 4 4 5 All those test are calculated using final unmodified SI component The main purpose of combined seasonality test is to check whether the seasonality of the series is DEMETRA User Manual doc 136 DEMETRA User Manual identifiable For example identification of the seasonal pattern is problematic if the process is dominated by highly moving seasonalit 2y The testing pr
60. ares the annuals 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 0 1 0 5 Severe 0 01 0 05 0 1 O J0 05 0 1 0 01 O e Visual spectral analysis Demetra identifies spectral peaks in seasonal ad trading days components using empiric criterion of visual significance For more information see the Annex e RegArima Residuals diagnostics 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 definitions of the residuals Demetra takes still another way similar to the solution developed in Stamp for instance The Annex 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 2 see appendix 3 which is distributed as a x 2 Results of the test Pi gt 0 01 0 1 o Independence test 18 In future versions of Demetrat it will be possible to choose the definition of the residuals that
61. ation F Calendar effects DEMETRA User Manual doc 51 DEMETRA User Manual 4 1 3 5 Outliers detection Both X 12ARIMA and TramoSeats detect outliers which are defined as the abrupt changes that cannot be explained by the underlying normality of the ARIMA model Three outliers types are detected additive outlier AO which affects an isolated observation level shifts LS which implies a step change in the mean level of the series transitory change TC which describes a temporary effect on the level of series after a certain point in timet comments Individual spec 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 different critical values for different outliers types Critical value outlier critical Critical value used in the outliers detection procedure AO J outlier ao Automatic identification of additive outliers Automatic identification of level shifts Automatic identi
62. ation of the unmodified SI component Friedman 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 large test statistics and small significance level indicates that a significant amount of variation in the Sl ratios is due to months or quarters respectively which in turn is evidence of seasonality DEMETRA User Manual doc 88 DEMETRA User Manual If the p Value is lower than 0 1 the null hypothesis of no seasonal effect is rejected Conversely a small F and large significance level close to 1 0 is evidence that variation due to month or quarter could be due random error and the null hypothesis of no month quarter effect is not rejected29 In the example above p Value is 0 0000 so the null hypothesis is rejected and it could be assumed that significant seasonality is present The second test for stable seasonality provided by Demetra is Kruskal Wallis test KruskKall Vallis test Kruskal Wallis statistic 162 5477 Distribution Chi2 11 P Value 0 0000 Stable seasonality present at the 1 per cent level The test s outcome stable seasonality present has confirmed the result from Friedman test The test for the presence of seasonality assuming stability uses the following decomposition of the variance S S4 S where k j E S gt X X
63. ault demetra If multi processing is saved in the workspace the multi processing s name is used 5 Additional functions 5 1 Changing the specification The user is able to modify the used specification and to see immediately the result of changes made The specification is 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 refer 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 DEMETRA User Manual doc 121 DEMETRA User Manual 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
64. ays Fired week 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 Calendar_1i Fixed day x 20 December Day of the month The data generated by each calendar can be viewed by a double click on the corresponding item in the workspace tree DEMETRA User Manual doc 22 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 1582 0 0 0 0 25 3 1382 1 l 0 0 4 1382 0 0 0 0 12 0 0 0 amp 1582 0 1 0 0 7 1982 0 0 1 0 8 1382 0 0 a 31382 0 0 0 bd r b k an am The regression variables can be inspected for any frequency monthly bi monthly quadric monthly quarterly half monthly yearly and any reasonable time span through that window the periodogram of those series are displayed when a column is selected Demetra presents three different views e Trading Days seven regression variables which correspond to the differences in economical activity between all days of the week and leap year effect e Working Days two regression variables which correspond to the differences in economical activity between the working days Monday to Friday and non working days
65. b 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 FINDLEY 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 HARVEY A 1989 Forecasting Structural Time Series Models and the Kalman Filter Cambridge University Press 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 2007 Guide to Seasonal Adjustment ONS Methodology and Statistical Development DEMETRA User Manual doc 145 DEMETRA User Manual HYLLEBERG S ed 1992 Modelling Seasonality Oxford New
66. c 113 DEMETRA User Manual workspace Once the output was created the user can save the multiprocessing The appropriate item will appear in the workspace tree oa gt Tramo Seats ES X12 ef X12Do0 1 4 4 2 3 Detailed results For each time series from multi processing seasonal adjustment Demetra offers the access to the complete description of the seasonal adjustment results by a double click on the time series name This option is available for both Processing and Matrix view panels The user can modify then 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 insufficient and the user wishes to modify some options to get a better result As an example the following panel shows how to change the pre specified outliers Lx X12 RSASc Dwellings competed p 0 000 Delay 0 063 i Jon Mar May Jul Seo Now Feb Agr JunAug Get Der DEMETRA User Manual doc 114 DEMETRA User Manual When the new options are chosen the user should click on Apply button to launch the seasonal adjustment with modified settings Series Method Estimation Processing Priority Quality Warnings Computed Unemployment TS R5A3 Concurrent Valid l x Sold production of industry TS RSA3 Concurrent Valid x CP
67. chosen model Only Box Jenkins SARIMA models p d q bp bd bq is considered Coefficients of the regular theta and seasonal btheta moving average polynomial Coefficients of the regular phi and seasonal bphi auto regressive average polynomial Parameters can be set if P or BP respectively is greater than 0 DEMETRA User Manual doc 62 DEMETRA User Manual 4 2 2 5 Outliers detection TramoSeats Comments Individual spec Argument iO IsEnabled Presence or not of the outlier individual spec os Outliers outlier span Span used for the outlier detection The span detection can be computed dynamically on the series for span instance Excluding last 12 obs Option outier a Describes the outliers considered in the automatic outliers detection It is possible to detect all types of outliers only AO additive outliers and TC transitory change or only AO and LS Default critical outlier critical When Use default critical value is false the 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 different critical values for different outliers types procedure regressor ML outlier imvx True if exact likelihood estimation method is estimation used false if fast Hannan Rissanen met
68. cide 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 added 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 here new time series to the multi processing DEMETRA User Manual doc 109 DEMETRA User Manual Multi processing definition wizard Choose series Series Specification Dwellings competed TS RSA5 Unempoyment rate TS RSA5 Add items Finishing The defined items series specification will be added tot the list of SA items in the multi senes processing At the last stage of the wizard Finishing the user can modify the name of
69. ct recursive processing Such an attempt will generate a crash of Demetra The example of recursive processing is to 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 possible Chart Grid List Table or Growth Chart Tools Container Chart ToolWindow Grid Options List p Growth Chart At first the user should choose one or few containers from menu DEMETRA User Manual doc 26 DEMETRA User Manual Workspace Seasonal adjustment Growth Chart Tools Window Help amp Tool Window Options eed Growth Chart Then the user can take any series or group of series from one of the browsers and drop it in a container Workspace Seasonal adjustment Growth Chart Tools Window Help a rrr Xml Excel Tsw usce POES CPICAPITALCITY CPI CHANGE e CRUDE PETROLEUM Morocco 4 ine EXPORTS EXPORTS FOB IMPORTS CIF IMPORTS CIF1 Fe Tunisia 7 MINING PRODUCTIO EXPORTS EXPORTS FOB IMPORTS CIF e IMPORT UNIT VALUE 4 b ih if 00 01 2005 01 2006 01 2007 01 2008 01 2009 01 201 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 series which appear in the results
70. d enor P yalue AO 4 2002 18 7046 3 41647 0 0000 LS 1 2007 38 5629 4 60194 Pre adjustment series Table presented in this section contains series estimated by Reg ARIMA part It includes interpolated series series adjusted for calendar effects deterministic component calendar effects trading days effect outliers effect on irregular component total outliers effect total regression effect Arima This section demonstrates theoretical spectrum of the stationary and non stationary model and autocorrelation function of the stationary part of the model DEMETRA User Manual doc 78 DEMETRA User Manual 1 1 0 8 05 o Oo 0 6 P 0 OL On ae 0 4 o 0 5 02 0 0 Pli2 Pl 10 20 30 Polynomials regular AR 1 0 34299 B 0 32833 B 2 seasonal AR 1 regular MA 1 seasonal MA 1 0 359335 Frequency of the regular AR roots 3 14159265358979 Regressors This section presents all regressors used in 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 LS 11 2008 0 occ amp e coioioioio i o io o 0 0 0 0 0 0 0 0 0 a Residuals The way in which Demetra calculates the residuals is presented in Annex Residuals from the model are presented in the graph and in the table DEMETRA User Manual doc 79 DEMETRA User Manual 0
71. de Could be changed by the program if needed H DEMETRA User Manual doc 54 DEMETRA User Manual 4 2 TramoSeats specifications The 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 4 2 1 General description TramoSeats Meaning spec file Transformation transform Transformation of the original series calendar specifically related to calendar Automatic modelling Automatic model identification Arima modelling Outliers detection Automatic outliers detection Options on the estimation procedure of the RegArima model Decomposition Seats Seats decomposition E 2 2 Transformation Comments Oot Fe spec Series sopan transform span Span used for the processing The span can be computed dynamically on the series for instance Last 90 obs Transformation of data logarithm or none Fct transform fct Control the bias in the log level pretest the function is active if lam Auto Fct gt 1 favors lev
72. des the full residuals defined by y X p or equivalently by L y X P The full residuals correspond to the one step ahead forecast error of the linearized series 1 2 X12 X12 provides the exact maximum likelihood estimates eml of the residuals However that sentence has to be clarified We first consider the model without regression variables When the stationary model is a pure MA model it is easy to derive the maximum likelihood estimates of the residuals they are defined for the period q n where q is the order of the MA polynomial 2 We give some more information on the handling of the general case which is less documented The software uses the following transformation Li afte P B y t 2 p where p is the auto regressive order To simplify the notation we will write below y for y foc and w for Z is We have that p y p z P Vo W p Yo Iw p w p w is solved by the solution developed for the pure MA case It generates a set of n p q residuals that correspond to the eml residuals of the transformed model We write them e Using well known properties of the normal distribution we can derive the distribution of P o w Indeed if we have that yLolw NCL w Dw KA L y C Lw C C can be easily computed using the Wald decomposition of the model The filtering algorithm of the pure MA model provides a transformation A such that A A Q So the initial residua
73. det_sa _f Deterministic effects det_t _f det_s _f det_i _f 17 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 DEMETRA User Manual doc 84 DEMETRA User Manual For those components in additive case the following relationships should be true MHE EE RMDE OMHE 1 CAL TDE MHE 2 OTOT OT 0OS 0OI 3 REGTOT REGT REGS REGI REGY 4 REGSA REGT REGI 4 DET CAL OTOT REGTOT 5 CT T OT REGT 6 CS S CAL OS REGS 7 Cl I OI REGI 8 CSA Y CS CT CI REGY 9 Y CT CS CI REGY T S 1I DET 10 Y Y DET T S TI 11 SA Y S T I 12 S Y T S4 I 13 The multiplicative model is obtained in the same way by replacing the operations and by Ux and respectively A first test in Basic diagnostic 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 initial series Q Results of the test gt 0 000001 lt 0 000001 DEMETRA User Manual doc 85 DEMETRA User Manual o Annual totals The test comp
74. e 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 window containing seasonal adjustment results TramoSeatsDoc 1 default calendar Default and user defined variables Variables DEMETRA User Manual doc 18 DEMETRA User Manual 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 01 1972 01 1976 01 1980 01 1984 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec DEMETRA User Manual doc 19 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 paragraphs below 3 1 Workspace menu 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
75. e final seasonally adjusted series the final trend with forecasts the final seasonal component with forecasts and the final irregular component Orginal senes Final seasonally adjusted senes Final trend compone Final seasonal Final irregula C Fi Final trend component forec 1 1991 8826 9920 93 10273 3 0 889635 0 9657 2 1991 10504 2 10736 7 07352 0 97a344 1331 7173 10731 4 11152 0 661698 0 967662 4 1991 8586 11744 11555 0 731099 1 01635 31 e724 12473 7 11856 5 1632 1 05206 1991 11795 12434 4 11962 0 948577 1 0395 7 1991 10358 11759 4 118820 8 0 680827 0 369783 1941 2618 10648 2 11687 5 0 809336 0 911081 915997 10104 12247 4 11483 3 0 852499 1 06654 10 19 10712 10784 9 113095 7 0393244 0 953596 11 19_ 12695 11165 2 11153 9 1 13701 1 00101 12 13 30360 11762 6 10345 1 2 63208 1 07463 S I ratio chart presents the final estimation of the seasonal irregular SI component and final seasonal factors for each of the period in time series months or quarters Curves represent the final seasonal factors and the straight line represents the mean seasonal factor for each period The SI ratio presented on the chart dots is modified for extreme values table D9 Final seasonal factors are calculated by applying moving average to the SI ratio from table D9 The results the final seasonal factors are displayed in table D1014 14 For more details refer to LADIRAY D and QUENNEVILLE B 1999 DEMETRA User Manual doc 74 DEMETRA User
76. e tree The users are strongly recommended to start their analysis as explained below with one of those specifications usually RSA4 c or RSA5 c and to change afterwards some of the options if need be For more advanced users Demetra offers an opportunity to create the new specifications and add them to the list This could be done by choosing the Seasonal Adjustment item of 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 used exactly like any predefined specification i im Single analysis E Workspace_1 at Mul ti P Toc ess ing F Single processing Tramo Seats LS xp El Trading days D AD Mutti processir El La mum kadi aci dpn Trading days E E TramoSeats Outliers detection RSAO Estimation i Decomposition Seats Pretest sign of trad Pretest on trading days correction Next two sections contain valuable information about the specifications The description of X12 specification is presented in 4 2 and the description of TS specification is presented in 4 3 Demetra is able to perform seasonal adjustment for one single t
77. els Fct lt 1 favors logs DEMETRA User Manual doc 55 DEMETRA User Manual Tramo Seats specifications Selection type Function E Arima modelling Fet Ol ters detection Fet Fct Controls the bias in the loglevel pretest Fet gt 1 favors levels Fet lt 1 favors logs 4 2 2 1 a effects Comments tem aa spec Type The user can choose between None Predefined Calendar UserDefined None means that calendar effects will not be included in the regression Predefined means that default calendar will 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 Trading days regression variables Acceptable values predefined e tdi include the weekday weekend type or calendar contrast variable type td2 include the weekday weekend contrast variable and a leap year effect td6 include the six day of he week variables td7 include the six day of he week variables and a leap year effect DEMETRA User Manual doc 56 DEMETRA User Manual TramoSeats Comments Individual spec Pretest regression aictest Pretest the trading days correction Option available for type P
78. 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 excel 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 i gt Resi DE i Save sa series Save calendar corrected series Save seasonal component XLS In addition to the options available for txt format using xls format the user can specify the layout DEMETRA User Manual doc 34 DEMETRA User Manual Save calendar comected series Save seasonal component Save trend Save iregular component Way A C D E F eT 2 Unempoyment rate Dwellings competed 3 01 01 1991 9916 368 01 02 1991 10498 27 5 01 03 1991 7 226337962 10747 64 6 01 04 1991 7 672831005 11737 07 01 05 1991 225091811 12478 14 8 01 06 1991 8 788001471 12440 98 9 01 07 1991 9 44489119 11767 94 10 a fiisa lsh vr CET ra Components are placed in the separate sheets gt ha Gotowy FA The option OneSheet will produce the following xls file DEMETRA User Manual doc 35 a demetra xls DEMETRA User Manual o x Ea anaana Dwellings ear Z 2 Orig 5 SA Orig S SA 3 01 01 1991 6626 0 590044 9916 366 01 02 1991 6239 0 784796 1049627 S 01 03 1991 f3 0 073662 7 226336 173 0 667402 10747 64 6 01 04 19
79. eneceeseneeeetes 11 2 1 OVERVIEW OT the SOWIE activins sonancessnsnsunsranihacs E E 11 L BON SCS aA E E ae nee eae 13 Da TOPPE TIO ae uniter cami nets vec iquasesanta piu ecauieumcanseatenntedvacacauiatenesucenoaet 16 Fh ORS A E sicrecrr ee sea nctcce seers sess E AE 16 2 NO aries satu sare pace oot dea saien faved sen neh ston aie E cuter Sante d eras E teeta canatonates 18 ZG RES ONES 10 NC aie cerca stteaaeeteeecc aseueieoas ate ndoota nsec soaseeeneostanncieseGtyyeness cass earseasdeecsaas 18 3 1916 erc hae om 2 Seana nee nee ener ree eee ae ee nnn ee eee cere eee eer 20 IL VOR See WONG ea E E easnenvedeenisonpaeace savant 20 Die ANGINA E AAE A AE EE A E E E E EE E E 21 3 1 2 User defined regression variables ccssccccsssecccesecccceesecceeeeseceeeeseceseeuscessusecessuneces 24 Bie MOOS HST A EE E A EE E E tad P tances sate bum essaqa mas E T AT 25 DAE LON g gare en een et E eae ee ee ere eee ee 26 322 OO b WIM W cere sxc ssavicacsetteanchsavet lt ceassuess beeen EE E 30 Ia SSOASOM A CHAM shi crctorancus oe cnst sevesmnettes soamesanates eto eeuueauunceddeatenreua tunanncaeneteretnials 30 I E SI CCU a IAI SIG eeanercceeutes ses erat E E ioaaetantedasnonancaesusesee 31 SW hee DIE ae een ee me E 31 Dee ODUN E E 32 3 2 2 4 1 Default SA processing output ssescseresreresureresreresunerrssreresuneresrererunserrsrenuns 33 LLA DOECNOS IC een ATE 33 DEMETRA User Manual doc 3 DEMETRA User Manual 32243
80. er Kolmogorov analysis Seats like Such solution leads 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 making 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 basic seasonal adjustment is straightforward However it is possible to use the API to solve very tricky problems A minimalist example is provided in the Annex DEMETRA User Manual doc 8 DEMETRA User Manual 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 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 adjust
81. f a workspace can be opened by a double click or by its local menu It is then showed in its previous state Demetra proposes several options to refresh it28 SAProcessing 1 Start Adel tems Gener abe output Quthers params Arima and outliers params Complete madel Parameters Only the parameters are refreshed The order of the ARIMA p d q P D Q is unchanged Outliers params Outliers and parameters are re estimated Last outliers params Outliers on the last periods and 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 28 For the moment those options are only available for multi processing DEMETRA User Manual doc 124 DEMETRA User Manual Annex 1 Definition of the residuals Several tests are built on the residuals of the RegArima model However what we mean by residuals is not so obvious TramoSeats and X12 use different definitions of residuals Demetra proposes another one Stamp like All those solutions correspond of course to the same likelihood their sums of squares are identical and they usually lead to very similar diagnostics However in some specific cases short series many regression variables and or missing values
82. fication of transitory changes t TC rate outlier crate 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 is 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 X12 10 KAISER R and MARAVALL A 2000 DEMETRA User Manual doc 52 DEMETRA User Manual M12 specifications Transformation Critical value Calendar effects El 4 1 3 6 Estimation Comments Individual spec Argument Precision estimate tol Precision used in the optimization procedure K12Spec 1 x Frecision DEMETRA User Manual doc 53 DEMETRA User Manual 4 1 3 7 a S 1 a adda agama co Comments spec Mode x11 mode Only additive mode Pseudo additive mode is not supported Use forecasts forecast maxlead 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 ba
83. 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 a 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 User variables from Workspace menu 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 Manual doc 24 DEMETRA User Manual 2 FI l G isiment Variables Tools Window Help a u a o S lA By ja Ye Odpowiedz ze zmianami Eames 0 RI UES SAH A XIZIRSAdc Source XCLPRVDR se hi fe ae l ae AEEA p aa na Pe A M PAO mayen Enay 3 ares eae eae z a z i 2 mal z The figures of static variables cannot be changed Currently the only way to update static series 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 Browsers X Varia bles TramoSeatsDoc 2 rx Xml Excel
84. gression USigma Artima modelling Outliers detection Automatic henderson filter Estimation Henderson filter 13 Decomposition X11 2 Advanced True 7 term False Seasonal filter The previous snapshot was realized by setting the Use forecasts option on false and the Seasonal filter on S3x15 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 SAProcessing 1 Edit Priority Save Initial order Update reports Generate output Current adjustment partial Concurrent adjustment Parameters Last outliers params All outliers params Arima and outliers params DEMETRA User Manual doc 123 DEMETRA User Manual The user still has to save the workspace using the usual menu command Save 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 whekspace Ty Ger O Open ld Save aif Save AS VILANPR DDFS MINGILSER S HOMEVPALATE h Demetra workspace 2 xml Ext A saved item o
85. gression vanable s used in the RegAnma model DEMETRA User Manual doc 57 DEMETRA User Manual Example calendar trading days Example user defined trading days ListSelector Example Easter effect DEMETRA User Manual doc 58 DEMETRA User Manual 4 2 2 2 Regression TramoSeats Comments Individual spec Argument Pre specified regression variables Corresponds to the pre specified outliers of outliers TramoSeats e aoyyyy pp e Isyyyy pp e tcyyyy pp rpyyyy pp zzzz qq Intervention regression variables Enables the user to define four types of variables intervention variables e Dummy variables e Any possible sequence of ones and Zeros l e of any sequence of ones 1 B and zeros 0 lt 0 Delta lt 1 l e W ofany sequence of ones 1 65 B and zeros 0 lt DeltaS lt 1 User defined regression user The user defined variables are input by the variables usertype user and can be considered as belonging to the trend to the irregular component or to calendar effects using the corresponding Is tc and holiday user types For practical considerations seasonal effects are currently not supported The user can specify the structure of the lags Example Pre specified outliers S Spec x Transformation Pre specified outliers 3 items Calendar effects Ramps 1 item j Intervention variables 2 items Arima m
86. h particular spreadsheet Xml Excel Tsw usce total number of time series in a workbook y ahir spreadsheet s name and the number of time series in it jeee CFI CHANGE hai CRUDE PETROLEUM PROS TION Moroco 4 E 2 INDUSTRIAL PRODUCTION ce MINING PRODUCTION s EXPORTS ce EXPORTS FOB z IMPORTS CIF IMPORTS CIF IMPORT UNIT VALUES IMPORT PRICES The 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 form 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 PET i Clear DEMETRA User Manual doc 14 DEMETRA User Manual If the user wants to put the workbook into cache memory he 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 Xml Excel Tsw usce DATADQRD2xds Insee xls Using 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 Simplify tree EXPORTS EXFORTS FHOHBH IMFORTS CIF IMPORTS CH IHFH Tunisie 7 Demetra is able to re
87. h row column corresponding to the same period or in the more compact form of horizontal lists of data DEMETRA User Manual doc 36 DEMETRA User Manual 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 O Txt series O Excel C ODBC d sarepository Iv List Cav matrix Seana y String Collection Editor Enter the strings in the collection one per line f Geres For example f D y 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 X 12 Doc This item is visible in the application s menu when X 12 seasonal adjustment was previously done and after that it was activated by the user DEMETRA User Manual doc 37 DEMETRA User Manual A12Doc 1 Specification Current specification Copy b 3 Paste Lack Addto workspace
88. he processing and for results that are usually very similar Diagnostics e Seasonality tests H Spectral analysis isions history Revisionpoligqy gt Parameters H Sliding spa Visible Nodes H Model stability Complete Outliers In the revisions history panels the user can have a complete overview of the different revisions for a given time span 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 Manual doc 93 DEMETRA User Manual tH AA tH Ht eH 2 07 1992 12 1992 05 1993 10 1993 03 1994 08 1994 01 1995 Export 993 Print b 07 1 Remove all Legend Paste Title JEBUG Demetra WorkspaceControl null Woiksp ct Settings 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 a g Fill sse lete Format 7 Sort amp Editing Q R CSA 2 1993 Revisions 2 1 1993 122 6861 3 1 1993 122 4878 4 1 1993 122 2625 122 0925 121 9857 121 9577 lt 5 1 1993 6 1 1993 7 1 1993 9577 8 1 1993 122 0333 9 1 1993 121 9712 10 1 1993 121 8328 11 1 1993 121 7152 12 1 1993 121 9291 1 1 1994 121 8648 2 1
89. he comparison of the results for Tile vertically option TramoSeatsDoc 1 Tools Window Help Floating Tabbed O Tieyerticaly ga TramoSeatsDoc 2 Charts M Tile horizontally Table a_ ___ BE Skinning p Pre processing Tramo 1 TramoSeatsDoc 1 ___ Pre adjustment series 2 TramoSeatsDoc 2 3 Arima Documents DEMETRA User Manual doc 39 DEMETRA User Manual Demetra offers six different skinning Ta Floating E Tabbed Tile vertically 0 Tile horizontally 1 TramoSeatsDoc 2 2X12Do0c 1 Documents 1 MacOS 2 Office 2007 Black 3 Office 2007 Blue 4 Orange 5 Vista The window menu includes also the seasonal adjustment processing done and not closed by the user during the current session Documents option offers some additional options helpful for organising windows I xi TramoSeatsDoc 2 Activate Close Document s Tile Horizontally Tile Vertically Cascade Arrange Icons Close DEMETRA User Manual doc 40 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 The description of the settings is available in the Annex The default specifications appear in the Workspac
90. he seasonal adjustment from time N to N isa sequence of R calculated in a following way34 Ay A A _ tlN tlt Riy 100 x tlt The revision history of the trend is calculated in a similar way Ly R y 100x tlN tlt tlt With additive decomposition R is calculated in the same way if all values A have the same sign gt Otherwise differences are calculated as Rin Any A tlt The analogous quantities are calculated for final Henderson trends 8 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 34 FINDLEY D F MONSELL B C BELL W R OTTO M C and CHEN B C 1998 35 X 12 Arima Reference Manual 2007 DEMETRA User Manual doc 142 DEMETRA User Manual SS Max zen z 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 For seasonally and trading days adjusted series the following statistic is being calculated ae j max A min A min A The value is considered to be unreliable if it is higher than 0 03 Similarly the seasonally adjusted changes are unstable if J J J A max min gt 0 03 A i t l 1 Whe
91. hod is El Outliers detection span Selection type Option Critical value EML estimation aio Describes the outliers considered in the automatic outliers detection AO additive outlier LS level shift TC transitory change DEMETRA User Manual doc 63 DEMETRA User Manual 4 2 2 a Estimation Comments tem a spec EML estimaton True if exact likelihood estimation method is used false if fast Hannan Rissanen method is used Precision estimate Precision used in the optimization procedure Uda p Unit root limit for final model x Transformation EML estimation True Calendar effects Precision 0 0001 Regression 0 96 Arima modelling 4 2 2 7 e Seats Comments Oo kem a spec Force model seats noadmiss When model does not accept an admissible decomposition force to use an approximation unit root seats When the modules of n estimated root falls inden ee in the range x 1 it is set to 1 if it is in AR if root is in MA it is set equal to xl ent ae Boundary from which an AR root is integrated in the trend component Tolerance measured in degrees to allocate tolerance AR roots into the seasonal component DEMETRA User Manual doc 64 DEMETRA User Manual Force model Calendar effects MA unit root boundary Regression Trend boudary E Arima modelling Seasonal tolerance Outliers detection Trend boudary mod Boundary from which an AR root is integ
92. i Excel TSw usce Processing Summary Matec view d tre bg Series Method Estimation Processing Priority Quality V 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 it won t be possible to update the processing Such variables are static so their location is not saved by Demetrat DEMETRA User Manual doc 117 DEMETRA User Manual Dene trae i E Microsoft Excel dataccds z Ba i ea ee Jai Series Method Estimation Processing Priority Quilty 1 9 o FE HICP XIRS Concuwent Unprce E BS lo l fe Depi conge MINAS Conamen E ari Sheet AS 1 Thea M3 3 HICP Linempoyrnent rate Sheet OS 495702 120 3126 HH 1991 04 129 0035 Drag drop series directly form external source unable refreshing results a ER 14 17 isj 1 16 d d 18 TS Properties Fal Name Empty Source Empty 3 When the multi processing was created the user should added it to the workspace and then saved it using the options from multi processing menu Then the user can use this multi processing for month to month quarter to quarter seasonal adjustment 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
93. ime series as well as for the whole set of time series First option is called single processing see 4 1 and is used for detailed analysis of the time series Second option called multi processing see 4 2 is a convenient tool for mass production of seasonally adjusted time series DEMETRA User Manual doc 41 DEMETRA User Manual 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 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 you should refer to the documentation of the original X12 program 4 1 1 General description item X42 spec file General options for the processing Transformation of the original series Specification of the part of the regression related to calendar not specifically related to calendar Automatic modeling Automatic model identification Arima modeling Outliers detection Automatic outliers detection Estimation estimate Options on the estimation procedure of the RegArima model Decomposition X11 x11 forecast X11 decompositio
94. indow 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 The user can change his hers choice of the active specification It enables to launch the seasonal adjustment for one time series using different specifications in order to compare the results DEMETRA User Manual doc 107 DEMETRA User Manual Processing Summary Matroc view Estimation Processing Priority Warnings Computed Concurrent Concurrent Valid 5 Unemployment Sold production of industry TS RSA3 x CPI CAPITAL CITY TS RSA5 Concurrent Valid x CRUDE PETROLEUM F TS RSA5 Concurrent Valid x definition Good 0 000 EXPORTS FOB 12 RSA3 Concurent Valid x annual totals Good 0 000 IMPORTS CIF 12 RSA3 Concurent Valid x IMPORTS CIF1 x 12 R5A5c Concument Walid x visual spectral analysis spectral seas peaks Good spectral td peaks Good spectral td peaks Uncertain 0 030 spectral seas peaks Uncertain 0 013 Unemployment 5A series 01 199501 199601 199701 1996 01 199901 2000 01 200101 2002 01 200301 200401 200501 200601 2007 01 200801 200901 201001 2011 New processing items C 1 0 0 1 1 ao 2 to 1 Is 2 The processing is actually launched by means of the Run command under the SAProcessing 1 main menu item
95. kspace panel organizes all specifications as well as the 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 apr may jun jul 2689 7 25994 2684 27208 2670 5 2567 9 25083 2466 2 2131 7 20438 20399 1989 1 1765 5 1695 4 1687 6 1683 1 2122 2 2073 1 2074 21164 2487 9 2445 4 24374 24776 2878 2841 1 2849 2 28715 3203 6 30646 3090 9 31059 3246 1 31596 31346 3123 3173 8 30925 30712 30424 2957 8 2867 3 2827 4 2809 2703 6 2583 2487 6 24434 2103 1 1985 1 1895 1 1856 1 1605 7 15256 14553 14229 1719 9 1683 4 1658 7 1676 1 1973 8 1907 9 1843 9 18128 RO N tw ww tO N N N function is 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 three Workspace g x Add New RS RS Exclude All RSA3 RSA4 RSA5 Tramo Seats Spec 1 El X12 currently active specification RSA3 RSA4c RSAS5c X12Spec 1 5j Calendars Default y User defined variables DEMETRA User Manual doc 16 DEMETRA User Manual The right click on any existing name opens the pop up menu which contains the following commands Open
96. le 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 Demetrat By means of right click menu the user can paste cut copy and delete time series marked Also priority can be changed into log based or level based DEMETRA User Manual doc 115 DEMETRA User Manual date reports Level based Log based Add to workspace Initial order The user can add new time series to the multi processing using Edit gt Add items option Add items Priority Generate output Add to workspace Initial order 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 Accepted DEMETRA User Manual doc 116 DEMETRA User Manual Series Method Estimation Processing Priority TS RSA3 Concurrent Valid 0 TS RSA5 Concument Valid 0 TS RSA5 Concurrent Valid 0 X12 R5 Concurrent Valid 5 SV2 RS Concurrent Valid 10 AV2 RS Concurrent Valid 10 TS Interactive Valid 0 Accept 4 5 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 a oo N Ee SAProcessing 1 xm
97. ls are computed as follows 30 See LJUNG G and BOX G 1979 or OTTO M C BELL W R and BURMAN J P 1987 DEMETRA User Manual doc 126 DEMETRA User Manual 1 Preliminary steps independent of the observations 1 1 Compute C 1 2 Compute A C by filtering the rows of C with the MA algorithm 2 Filtering 2 1 Compute w 2 2 Compute Aw with the ma algoritm 2 3 Multiply the results from 1 2 and 2 3 and subtract it from the p first observations 2 4 Pre multiply those residuals by the inverse of the Cholesky decomposition of de variance matrix of y Olw easily obtained from 1 2 the result correspond to the first p residuals Those residuals can be interpreted as the one step ahead forecast error of y knowing w We note them e The complete set of the residuals are then e e When the model contains regression variables X12 X13 uses an iterative procedure in a first step for given coefficients it computes the linearized series and it estimates by ml the parameters of the arima model for that series in a second step it re estimates the coefficients of the regression parameters for the new model and it goes back to the first step The final residuals are obtained from the linearized series by the procedure explained above when the iterative procedure has converged 1 3 Demetrat In Demetrat the residuals are the one step ahead forecast errors of the state space model that contains the coefficien
98. matrices can be copied into the clipboard by the usual keys combination Ctrl C for user 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 updates 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 Priority offers two options level based and log based Save saves the processing Generate output offers many 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 After defining a multi processing the user should run the estimation After that it is possible to generate output The save option is inactive as soon as the user adds the processing to the DEMETRA User Manual do
99. ment 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 Uninstall previous version of Demetra In order to remove any previously installed Demetra version the user should take the following steps Open the Add Remove Programs function in the control panel Uninstall Demetra if listed Close the Add Remove Programs function Delete the Demetra home directory Delete the program group icons if manually created 1 3 Installing Demetra Execute the file setup and follow the instructions on the screen Always take the default options i e typical installation etc 1 4 Running Demetra Start working with Demetra run Demetra via the newly installed Windows option under Programs or start the Demetra exe file directly from the Demetra sub folder DEMETRA User Manual doc 9 DEMETRA User Manual 1 5 Closi
100. 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 Working Day using one parameter specification working vs non working days DEMETRA User Manual doc 129 DEMETRA User Manual Trading days a pretest is made for the presence of Trading Day using six parameters specification for working days the day of week Monday Fridayis specified Easter the program tests for the necessity of a correction for Easter effect in the original series Outliers detection Demetra automatically detects all types of outliers including AO additive outliers LS level shifts TC transitory outliers 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 4 Tests 4 1 Doornik Hansen test The Doornik Hansen 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 B 3 n 27n 70 n 1 n 3 n 2 nt 5 n 7 n 9 1 2 B 1 l J0 5log 1 n 1 n 3
101. must be used in the tests and displayed in the graphical interface Obviously the choice is more a question for purists DEMETRA User Manual doc 86 DEMETRA User Manual The independence test is the Ljung Box test see Annex 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 Pir woe 0 01 0 1 O Spectral tests Demetra testing the presence of the trading days and seasonal peaks in the residuals For this purpose the tests based on the periodogram of the residuals for the trading days frequencies and for the seasonal frequencies are implemented The periodogram is computed at the so called Fourier frequencies which present good statistical properties Under the hypothesis of Gaussian white noise of the residual it is possible to derive simple tests on the periodogram around specific groups of frequencies The exact definition and the used test are described in the Annex Results of the test P stat gt val lt 0 001 0 001 0 01 0 01 0 1 e Residual seasonality diagnostics The residual seasonality diagnostics correspond to the tests developed in X12 The F Test on stable seasonality see Annex is computed on the differences of the seas
102. n 4 1 2 Basic Comments Individual spec Pre processing Enable Disable the other individuals specs except X11 series Series span span Span data interval of the available time series used for the processing The span can be computed dynamically on the series for instance Last 90 obs Specifications X12Do1 Pre processing gt Transformation O Series span z Calendar effects Selection type Regression H Arima modelling s Outliers detection Z Estimation Bi Decomposition 411 Excludin nit election type a DEMETRA User Manual doc 42 DEMETRA User Manual 4 1 3 Transformation Comments Individual spec Argument Transformation transform function Demetra accepts the following options e None e Log e Auto AIC Difference Disabled when the transformation is not set to Auto Adjust hill 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 X12Doc 1 Specifications Transformation z Transformation AIC Difference Calendar effects 5 Regression ET e Dutliers detection LengthofPeriod 2 Estimation oe Decomposition 11 Adjust Preadjustment of the senes for length of pernod or leap year effects The senes is divided by the specitied effect Not available with the 4 1 3 1 Calendar effects F Comments Individual
103. n k Where 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 DEMETRA User Manual doc 134 DEMETRA User Manual 4 4 2 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 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 k w SF 3
104. n of the plotted values of s A and must be larger than both neighboring values s A _ and s A by at least 6 52 A A times the range s s min For a given series Yr 0steD which may contain missing values the periodogram is computed as follows In a first step the series is standardized Y Y O y Li 2m T 1 Gs oaae In a second step we compute at the so called Fourier frequencies 2 which are the values of the periodogram 2 N t lt T i Z e t 0 z defined cot where is the number of non missing values Under the white noise hypothesis 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 365 25 q Cla Other frequencies correspond to trading days frequencies q 4 DEMETRA User Manual doc 141 DEMETRA User Manual e For monthly series 2 714 default 2 188 e For quarterly series 1 292 1 850 2 128 default 0 280 7 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 A and a later adjustment based on all data span most recent adjustment denotes tlt as Aj In case of multiplicative decomposition the revision history of t
105. nal trend with forecasts o the final seasonal component with forecasts othe final irregular component o 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 seasonal factors are presented in the S ratio chart 4 3 2 2 2 Pre processing Table presented in pre processing section contains series estimated by Tramo part It includes interpolated series series adjusted for calendar effects deterministic component calendar effects trading days effect outliers effect on irregular component and total outliers effect Arima section shows theoretical spectrum of the stationary and non stationary model and autocorrelation function of the stationary part of the model Regressions section presents all regressors used in Tramo part including trading days variables leap year effect outliers Easter effect ramps intervention variables user defined variables In the next part the one step ahead residuals from the model are presented both in the graph and the table Analysis of the residuals consists of several tests and residuals distribution For details please refer to seasonal adjustment results for X 12 ARIMA and to Annex 4 3 2 2 3 Decomposition The decomposition made by Seats assumes that all components in time series trend seasonal and irregular are orthogonal and could be modeled using ARIMA model Identification of the
106. ng 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 created any unsaved work Demetra will warn you and provide you with the opportunity to save it DEMETRA User Manual doc 10 DEMETRA User Manual 2 Main application s windows 2 1 Overview of the software When the user launches the program he she should see the Demetra window lox Workspace Seasonal adjustment Tools Window Help Browsers X Xml Excel Tsw usce New Open Save Paste 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 acentral 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 next paragraphs Panels can be moved resized superposed and closed depending on needs or preferences of the user The presentation is saved between different sessions of Demetra The application can contain multiple documents Depending on the needs the user can present
107. nt to activate DEMETRA User Manual doc 65 DEMETRA User Manual e Open the local menu by means of the right button of the mouse e Choose the Active option from pop up menu Workspace E p Workspace_1 i d Single processing a TramoS eats Ly 12 ae de Mult processing d Specifications El Trams eats l i FSA Open Exclude Delete Clone af Calendars ee Default Baie te User defined variables 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 e f some single processing are open i e single processing windows have been opened in the central panel they are updated with the new series DEMETRA User Manual doc 66 DEMETRA User Manual ur Gemetra Workspace Seasoral adjustment TramoSeatsDoc 1 Tools Window Help Xm Ee Tsw use 3 d E TranosSeatsDoc 1 e f no unlocked single processing is available a new one is generated with the active specification 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 emmetra 4 Wietopece Sessomal adjustment X1fDec 3 Tods Window Help roses a X xmi Exel Tsw ust g ti
108. nth in each span For the tests description see Annex DEMETRA User Manual doc 95 DEMETRA User Manual 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 10 1 1037 Detailed results of sliding spans analysis conducted separately for seasonal component trading days effect and SA series changes are presented in three graphs Upper panel shows the sliding spans statistic for each period the bottom left panel presents the distribution of sliding spans unstable periods months or quarters Bottom left panel contains detailed information about the percentage of values for which sliding spans condition is not fulfilled It gives idea weather observations with unreliable adjustment cluster in certain calendar periods 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 is less than 15 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 DEMETRA User Manual doc 96 DEMETRA User Manual 1 5 0 5 0 01 2001 01 2002 01 2003 01 2004 01 2005 01 2006 01 2007 01 2008 01 2009 Abnormal values 3 1 Distribution 40 00 Breakdowns of unstable factors and Average Maximum
109. o spectral estimators periodogram and autoregressive spectral estimator After choosing one of them from Tools menu the empty window is displayed Container F TS Properties Options Chart La TEN Seasonal chart Periodogram To calculate periodogram drag and drop a raw time series into the displayed window The methodological note about spectral analysis is available further into this instruction x 3 2 2 3 Differencing Differencing window gives the access not only to the table and spectral graphs but also to ACF and PACF functions for selected time series To do it the time series from the list should be dragged and dropped into Name box 7 For more information see Annex DEMETRA User Manual doc 31 DEMETRA User Manual Differencing estimate button EXPORTS 2000000000 b y i 8 E i b Ti Py a 2000000000 4000000000 01 1955 01 1965 01 1975 014 4985 01 4995 01 2005 01 1960 04 4970 01 1980 01 1990 01 2000 01 2010 Using the bookmarks on the right the user could switch other functions like periodogram and auto regressive spectrum autocorrelation function and partial autocorrelation 3 2 2 4 Options The window contains the default options used by the Demetrat The initial settings can be modified by the user The menu includes setting for workspace default processing output settings for the browsers DEMETRA User Manual doc 32 DEMETRA Use
110. ocedure is shown below 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 0 5 0 5 7 _3Fy 7 Fu F F F F 2 S ee Failure if T 2 1 7 3 F Failure if 2 1 o gt 1 S S 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 32 DAGUM E B 1987 DEMETRA User Manual doc 137 DEMETRA User Manual 5 X 12 ARIMA 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 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 SI Values Table
111. odelling User defined variables litem Outliers detection sonata x Decomposition Seats Is 7 2002 Year 2010 ao 1 2000 Period 5 Type TC 11 For more details and examples see MARAVALL A 2008 DEMETRA User Manual doc 59 DEMETRA User Manual Example Ramps RampProperties Example Intervention variables DEMETRA User Manual doc 60 DEMETRA User Manual Example User defined variables TramoSeatsSpec 3 x Var 1 1 2 Varnable War_1 First lag 4 2 2 3 Automatic modeling TramoSeats Comments Individual spec Argument IsEnabled Presence or not of the automdl individual U U a spec b1 automdl ub1 Initial unit root limit in the automatic differencing procedure Pcr differencing procedure Cancelation limit for AR and MA roots automdl pcr Ljung Box Q statistic limit for the acceptance of a model Minimum t for significant mean TramoSeatsSpec 3 ls enabled DEMETRA User Manual doc 61 DEMETRA User Manual 4 2 2 4 Arima Options included in this section are active only if IsEnabled parameter from Automatic modeling section is set to false tem a spec Mean regression variables a n oe BP BD _ o Tra a 7 Calendar ae Comments It is considered that the mean a constant term is part of the Arima model it highly depends on the
112. old production of industry TS RSA3 Concurrent Valid l x CP CAPITAL CITY TS RSA5 Concurrent Valid l x CRUDE PETROLEUM F TS RSA5 Concurrent Valid x definition Good 0 000 EXPORTS FOB A12 RSA3 Concurrent Valid x annual totals Good 0 000 IMPORTS CIF1 12 RSA3 Concurrent Valid l x IMPORTS CIF1 A12 R5A5 Concurrent Valid Good l x visual spectral analysis spectral seas peaks Good spectral td peaks Good normality Good 0 234 eae independence Good 0 262 Unemployment 5A 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 tofi Is 2 The Summary panel gives general information on the results obtained from each method for each frequency 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 Manual doc 111 DEMETRA User Manual ze SAProcessing 1 loj x 7 pe number of series 4 Transformation iasi Log transformations 3 75 00 Arima models 3 1 0 0 1 1 1 25 00 1 1 0 0
113. on of the components second column with theirs estimators The trend estimator always has a smaller variance 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 variations of a relatively stable will be extremely underestimated2 Vanance Tonponent stinatorTestinaie vane frend oen 0 2090 osa ooo se 071 8 0 5978 0 5553 seasonal 5 1675 0 1904 0 1585 Doa For each component Demetra exhibits the values of the twelve consecutive lags from lags 1 to lags 12 autocorrelations its theoretical MMSE minimum mean squared error estimator estimator and estimate actually obtained Comparison of the theoretical MMSE estimator with the estimate actually calculated can be used as a diagnostic tool The close agreement between estimator and estimate points towards validation of the results24 22 MARAVALL A 1995 23 See MARAVALL A 1993 24 GOMEZ V and MARAVALL A 2001 DEMETRA User Manual doc 102 DEMETRA User Manual trend 4 fomo oos O ooz fosses e fomm ooa oo os e fomo foma ooz oes e foomo oos oos oms a fomo foomo oos osrs C C C e E e fomm foomo ooms ossz e fomo foomo ooma ono irregular C C E a zee s foom ooa ooma ooms e foom oo oomo oss e fomo foon oor pss The decomposition made by SEATS assumes
114. onally adjusted series Component CSA see above and on the irregular 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 1 9 For the seasonally adjusted series one test is computed on the complete time span and another one on the last 3 years 19 DAGUM E B 1987 DEMETRA User Manual doc 87 DEMETRA User Manual Results of the test Pr F gt val 0 01 0 05 Bad 0 05 0 11 e Number of outliers 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 was detected above 3 according to the table the chosen ARIMA model cannot fit all of the observations Results of the test Treshold 0 05 0 1 0 03 0 051 e WM statistics For the test results refer to 4 3 2 1 3 Seasonality tests The diagnostic section includes the set of seasonality test useful for checking the presence of seasonality in time series Those tests are described in Annex The seasonal component includes the intra year variation that is repeated constantly stable seasonality or evolving from year to year moving seasonality To determine if stable seasonality if present in a series Demetra computes Friedman test using the seasons months or quarters as the factor on the preliminary estim
115. ose different filters for each specific month to do a preadjustment of the original series with prior adjustment factors to specify ARIMA model p d g P D Q without some lags in the regular part The User s Manual is divided into five parts Chapter 1 presents the general features of the software and installation requirements In Chapter 2 the application s menu is outlined It is also shown how to visualize the data provided with the software and how to import new series from Excel Chapter 3 focuses on workspace menu and useful options offered by Demetrat Chapter 4 describes how to define the seasonal adjustment of a single series and many series In this part the result of seasonal adjustment is discussed Some detailed aspects like description of the tests and some technical issues are described in the Annex 4 For example the user cannot specify the model 2 1 1 0 1 1 without parameter AR 1 DEMETRA User Manual doc 7 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 a tool to search outliers in an Excel worksheet containing time series Demetra XL a seasonal adjustment tool in the Microsoft Excel environment inspired by the Demetra which can be used for multiprocessing XL Functions Set of Demetra Excel functions The add ins are described in the documentation attached
116. ox Plerce on squared residuale 24 DEMETRA User Manual doc 80 DEMETRA User Manual 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 null hypothesis was rejected There is an evidence of autocorrelation in residuals A linear structure is left in the residuals Demetra also presents residuals distribution In this section autocorrelation and partial autocorrelation functions are presented Autocorrelations tthe 1 ry ey 0 1 0 4 5 10 15 20 25 30 35 03 0 2 Partial autocorrelations 0 2 0 1 4 3 2 1 3 Decomposition Tables In this section all important tables from X 11 procedure are available The view of B tables is presented below feb mar apr may jun jul aug sep oct nov dec 0 0 0 2 48333 1 654 0 876 0 0 0 0 2 900 0 42234 0 o ES m0 0 0 0 1 161 0 1454 0 0 Transpose 0 0 0 0 Reverse chronology 0 0 006 0 0 Print 0 J 7 0 0 o 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 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
117. ponds 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 Time series are identified by their names Currency M1 67865 96 6366053 63625 74 65497 64 6663533 6903324 1672 27 74386 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 Information like data periodicity starting and ending period can be derived from the first column After they have been copied in Excel the data can be integrated in Demetra as follows e Select the Xml panel in the browsers 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 DEMETRA User Manual doc 12 DEMETRA User Manual e Change the names
118. r Manual formatters for txt and xml files settings for presentation the diagnostic where the user can change the critical values and other parameters for diagnostic tests outputs where the folder that will contain the results is specified Some of those functions are discussed below 3 2 2 4 1 Default SA processing output The user can decide which parts of the results will be presented after 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 the items are displayed after SA processing The picture below presents that two diagnostic will not be visible in the SA results az Al click here XCLPRVDR ODECPRYDR Show Hide result TramoSeats SdmoxProvider BHO Main result TSW USCB Xml choose the results you Tat would like to show hide lf Preprocessing Tramo AML Spreadsheet Tat 3 2 2 4 2 Diagnostic This part includes information about significance level for tests result 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 The default settings for the tests can be changed by the user DEMETRA User Manual doc 33 DEMETRA User Manual E OK Caned 3 2 2 4 3 Outputs This section
119. rated in the trend component 4 3 Single processing Demetra offers several ways to define seasonal adjustment of a single time series A first question which will determine the best way to proceed concerns the specification 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 he wants to integrate systematically its own calendar variables or if he 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 wa
120. re A k the seasonally or trading day adjusted value from span k for month t N1 t k period t and t 1 are in the k th span 9 Code to generate simple seasonal adjustments C Some namespaces have been removed to simplify the reading creates a new time series parameters fregquency 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 O g_prodind false basic processing tramo seats specification RSA5 full automatic TramoSeats Specification ts_spec TramoSeats Specification RSA5 launches tramo seats core engine TramoSeats Monitor ts_monitor new TramoSeats Monitor executes the processing TramoSeats TramoSeatsResults ts_rslts ts_monitor Process s ts_spec x12 specification equivalent RSA5 full automatic X12 Specification x_spec K12 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 DEMETRA User Manual doc 143 DEMETRA User Manual 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 computes statistics on the differences DescriptiveStatistics stats new DescriptiveStatistics diff Values
121. redefined Holidays When the user chooses the calendar type calendar type for the trading days he must specify the corresponding holidays It should be noted that such a holiday must have been previously defined see 3 1 1 Items regression When the user chooses for the trading days UserDefined type the type UserDefined he must specify the corresponding variables It should be noted that such variables should have been previously defined see 3 1 2 Easter regression variables The option enables the user to estimate the IsEnabled and or Easter effect in tree different ways aictest The user can choose between e No e Pretest e Yes No a correction for Easter effect is not performed Pretest meant that Demetra tests for the necessity of a correction for Easter effect 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 Length regression easter w Duration of the Easter effect w parameter of the easter variable The current version of Demetra doesn t allow the use of stock trading days Regression variables for the handling of Labor Day and of Thanksgiving are not handled Example predefined trading days Tacha ading day in use Calendar effects Type Predefined H Arima modelling Outliers detection Estimation Decomposition Seats Duration trad Defines the trading days re
122. riodogram at the Fourier frequencies cccsscccccsssccecesssececeenecesseeceesaeeeees 132 4 33 Teston theperiddograM siascisctitasths Rawaiceluda teguals SeossisncoeedateaSecascnageautereoniecasaae 132 4 4 SO ASO AINOY LCS Taaa E 133 4 4 1 Friedman test stable seasonality test eesccccccsssseeecceeeeeseeceeseeeeeeeeeeenes 133 44 2s Kr skal Walis test cinsa saxetateanbewbus auton AN 135 4 4 3 Test for the presence of seasonality assuming stability eeseeeseeeeeererneen 135 4 4 4 Evaluative seasonality test Moving seasonality test ccccccccesessseeeeeeeees 135 4 4 5 Test for presence of identifiable seasonality cceccccessececceeseceeeeeeeeeeeeeeees 136 4 4 6 Combined seasonality test cccccccssseccccssececceseccceeseececeeeceseeecesseeeeeseeeeeses 136 Ds eo 2ARIIV I Re TAD OS vescadessacasdevacsasssveccetassacetadesbaseadav asus nacedlewiuseada lacsuadaareesuadaeeanesesnaiies 138 6 Visuakspectral ANALY SIS ccomsarsecesacsincsadssetedunccnedatnasbadavadsasas nldoadeunteesedeancasasbuweseadawa vecctunsceecs 140 The REVISION AIS COG OS seca taeda desicceca saccade E 142 Oe SINUS SA e aa cece ot nastars wane sodieve sae arneaee poset anand vad cna E 142 9 Code to generate simple seasonal adjustments C ceeccsceeeccsseeeeseeeeeeseseeeeeseees 143 REFERENCES onran 145 DEMETRA User Manual doc 5 DEMETRA User Manual Introduction Seasonal adjustment SA i
123. rity 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 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 0 8 0 6 0 4 0 2 Jan Feb Mar Apr May Jun Jul Aug Sep Oct Mov Dec 4 3 2 1 2 Pre processing First part of the pre processing output includes information about data estimation Span 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 The charts below presents exemplary tables taken from different series DEMETRA User Manual doc 76 DEMETRA User Manual Data transformation Estimation span 1 2000 1 2010 Model tion Number of effective observations 108 Number of estimated parameters 11 Loglikelihood 329 7318 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 are presented In the example below the Arima model 0 1 0 0 1 1 was chosen which means that only one seasonal moving average par
124. s 8 2008 Regression Ramps 1 item 2010 02 01 2011 05 01 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 DEMETRA User Manual doc 49 DEMETRA User Manual 4 1 3 3 Automatic modelling X12 Comments Individual spec IsEnabled Presence or not of the automdl individual Spec Accept default 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 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 Hannan Rissanen 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 limit ArmaLimit automdl armalimit Threshold value for t statistics of ARIMA coefficients used for final
125. s an important step of the official statistics business architecture and harmonisation of practices Since the 1990s the Eurostat has been playing a role in the promotion development and maintenance of an open source software solution for seasonal adjustment in line with established best practices In 2008 European Statistical System ESS guidelines on seasonal adjustment have been endorsed by the CMFB and the SPC as a framework for seasonal adjustment of PEEls and other ESS and ESCB economic indicators ESS guidelines focus on two most commonly used seasonal adjustment methods TramoSeats and X 12 ARIMA2 and present useful practical recommendations The aim of creating new seasonal adjustment software Demetra was to supply a flexible software solution which covers the recommendation of ESS guidelines in this area Demetra was 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 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 ARI
126. s pedeaana masoatanonmuauahetuacednsiasean laa 62 422 50 Outliers CELE CUON x pisisc choice aces eh eee E dames aah 63 4220 TESUIMOUION snichedsataaveoiecuronsieb comet acentsmtuenesiauaabuouaiey eleaunc us Soatenentoaucantrdiavudensuaseanuleds 64 4 2 2 7 DECOMPOSILION SCAUS shinee acs seed ad sedate NNS 64 4 3 Single DKOCESSI Nene eicccas wuenta evan icuia aan E aud atta E A E 65 4 3 1 Defining a SINSIE plOCESSING cuers a audi R ova ane eeee 65 4 3 1 1 Creation of a single processing using existing SPECIFICATION ccccceeeeeeeeeeees 65 4 3 1 2 Creation of a single processing by defining new specifications eseese 68 4 3 2 Seasonal adjustment results single processing cccceseececcsseccceescceeeeseceeeeness 70 ral a 2p Sam A ZARIA rer ee eT es eee eee 72 ALE Mnre Ues a a a a 73 A2 L2 IPVS DFOCESSIMG sianet oa a A 76 4S 2 L3 DECOmpPOSIHUO Neien a T a N 81 A2 Lk DIINO tC ea a a 83 A S22 1 TAVMIO e aS A E A eea vealed eeaei et ee taeetiel econ 99 A322 Man FOSUINS nse a a ohiadetansvae betel AR 100 A22 PRO DFO CESSING ana A adel Soe ions 101 DEMETRA User Manual doc 4 DEMETRA User Manual A322 DECOMPOSE R 101 A2 2A DIENOS tICS icn a a E lukas 106 AA MUL O COS SING orreri ai a a A S 106 4 4 1 De TIMING SUIS DT OCOSSING arinean N ANNEN 107 4 4 2 Seasonal adjustment results for MUItI DrOCESSING ccccceeeccceeececeeeceeeeceeeuees 110 A Ads GENETIES aer a a Resta dats aes cane See teea ee eee 110
127. sic options is used to extend the series LSigma sigmalim First parameter of sigmalim lower sigma boundary for the detection of the extreme values Seasonal filter USigma sigmalim Second parameter of sigmalim uppersigma boundary for the detection of the extreme values seasonalm Specifies which seasonal moving average seasonal filter will be used to estimate the seasonal factors mm a seasonal filters periods Automatic 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 Sigma Vector 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 1 x n Basic E 0 Basic Z Transformation Multiplicative z Calendar effects Use forecasts True Regression E 1 General Arima modelling Automatic henderson filter True 2 Automatic modetliric Henderson filter i Arima LSigma Outliers detection Seasonal filter Estimation U Sigma Decomposition mo
128. sidual 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 Demetra provides spectral plots to alert the user to the presence of remaining seasonal and trading day effects 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 from Tools menu see 3 2 DEMETRA User Manual doc 90 DEMETRA User Manual Two spectrum estimators are implemented periodogram and auto regressive spectrum21 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 monthly series the frequency 3 corresponds to a periodicity of 6 months The trading days frequencies are described in Annex Peak at the zero frequency corresponds to the trend component of the series 40 Periodogram i 0 Pli2 Pl Auto regressive spectrum 0 Pli2 Pl At seasonal and trading days frequencies a peak in model residuals indicates the need for a better fitting model In particular peaks at the seasonal frequencies are caused by inadequa
129. sis is described in e g MARAVALL A 1993 MARAVALL A 2008 MARAVALL A 2006 MARAVALL A 1995 DEMETRA User Manual doc 104 DEMETRA User Manual Trend Cycle Seasonally adjusted Sessone Irregular 35 30 25 20 15 10 5 0 Squared gains indicate which frequency components of the data are suppressed or amplified by the filter Squared gain values larger than one suggest that the corresponding frequency component is stronger in the estimate than in the component at least in the sense of contributing more variability Phase delays indicate how frequency components are shifted in time by the filter Phase function is calculated for trend cycle and seasonally adjusted series to evaluate how much seasonal filters delay business cycle information2 26 See FINDLEY D F MARTIN D E K 2006 DEMETRA User Manual doc 105 DEMETRA User Manual Lag Trend Cycle Seasonally adjusted Seasonal Transitory Irregular Frequency response WK fiter ACGF stationary Square gain function Phase effect The Decomposition panel contains the ARIMA models which are defined by SEATS The sub panels of that part of the output present for SEATS many properties of the Wiener Kolmogorov filters generated by the canonical decomposition 4 3 2 2 4 Diagnostics Demerta offers the following seasonality tests o Friedman test o Kruskal Wallis test o Test for the presence of seasonality assuming stability
130. spec AICC Difference regression aicdiff Demetra only considers pre tests on regression variables related to calendar effects trading days or moving holidays Type The user can choose between None Predefined Calendar UserDefined None means that calendar effects will not be included in the regression Predefined means that default calendar will be used Calendar corresponds to the pre defined trading days variables modified to take into DEMETRA User Manual doc 43 DEMETRA User Manual Comments a en spec 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 Pretest regression aictest Pretest the significance of the trading days regression variables using AICC statistics Trading days regression variables Acceptable values predefined type or calendar type e Td include the six day of he week variables and a leap year effect td1Coef include the weekday weekend contrast variable and a leap year effect tdNoLpYear include the six day of he week variables tdiNoLpYear include the weekday weekend contrast variable Some options can be disabled when the adjust option is used in the transformation specification Length of period regression variables Accept
131. t 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 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 presented in the following table 12 Description from CAPORELLO G and MARAVALL A 2004 DEMETRA User Manual doc 70 DEMETRA User Manual Meaning of the quality indicator Vole Meaig _ V The quality is undefined because of unprocessed test meaningless test failure in the computation of the test etc Error There is an error in the results The processing should be rejected for instance it contains aberrant values or some numerical constraints are not fulfilled Severe There is no logical error in the results but they should not be accepted for Pree a nn nt ue te seer Or Bad The quality of the results is bad following a specific criterion but there is Pn atualerorandtne resutseoudbeused nn ee Several qualitative indicators can be combined following the basic rules Given a set of n diagnostics the sum of the results is There is at least 1 severe diagnostic but no error S Bad No error no severe diagnostics
132. t Fe A and f s A are uncorrelated N 0 1 random variables n n 4 3 3 Teston the periodogram Under the hypothesis that z is a Gaussian white noise and considering subset J of Fourier t frequencies we have DEMETRA User Manual doc 132 DEMETRA User Manual a J Shout AA S nk pet jeJ f 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 6e 2m6 m6 ao o Ao 1 292 1 850 2 128 where d is computed as follows if s is the frequency of the series 365 25 n S d n modulo 7 4 4 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 4 4 1 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
133. te 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 from 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 21 The theoretical motivation for the choice of spectral estimator is provided by SOKUP R J and FINDLEY D F 1999 DEMETRA User Manual doc 91 DEMETRA User Manual Revision histories Revision history is stability diagnostic which visualise how a time series is affected when new observations are introduced This statistics is generated both for SA series and trend cycle component For each point the revision history shows the initial adjustment obtained when this point is the last observation in the time series blue circle and the later adjustment based on all available observations at present red line The difference between those two values is called a revision As a rule smaller revisions are better 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 accept
134. tested Friedman test requires no distributional 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 31 Unmodified Seasonal Irregular component is the seasonal irregular factors with the extreme values DEMETRA User Manual doc 133 DEMETRA User Manual 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 Dj x x0 e a j l i l ie where Xk the average of k th sample The total variance is therefore broken down into a variance of the averages due to seasonality and a residual seasonality The test statistics is calculated as k 2 D nj Aj Aee j l E s 1 F k 1 n k DD ig aay j l i l
135. the file s name nor its location 2 Start Demetrat 3 Chose the multi processing from the workspace tree by double clicking on it Elm Single processing TramoSeats E gt x12 iad a 12Doc 1 a Default oo User defined variables 4 Choose in which way you would like to refresh the results2 27 For more details see 5 2 DEMETRA User Manual doc 118 DEMETRA User Manual Jt La fa a l i Current adjustment partial P Partial concurrent adjustment Parameters Concurrent adjustment Last outliers params Priority 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 emh 6 Choose the option Generate output form the menu Update reports Refresh Edit Priority Initial order 7 Mark the output and click OK DEMETRA User Manual doc 119 DEMETRA User Manual Save calendar comected series Save iregular component Save original series Save sa sees Save seasonal component Save trend Csv matrix VerticalOrentation Folder Defines the folder that will contain the results 8 Demetra 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
136. the outcomes Pre i nima Estimation span 1 1991 12 2008 Series has been log transformed No trading days effects Easter effect detected 3 outliers detected definition Good 0 000 annual totals Bad 0 063 visual spectral analysis spectral seas peaks Good spectral td peaks Good reganma residuals normality Good 0 740 independence Good 0 927 spectral td peaks Uncertain 0 093 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 0 074 m statistics gq Good 0 437 q without m2 Good 0 456 In 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 Manual doc 73 DEMETRA User Manual 50000 40000 30000 20000 UPOD eS ALA A dada dee 0 01 1991 01 1993 01 1995 01 1997 01 1999 01 2001 01 2003 01 2005 01 2007 01 2009 01 1992 01 1994 01 1996 01 1998 01 2000 01 2002 01 2004 01 2006 01 2006 01 2010 01 1991 01 1993 01 1995 01 1997 01 1999 01 2001 01 2003 01 2005 01 2007 01 2009 01 1992 01 1994 01 1996 01 1998 01 2000 01 2002 01 2004 01 2006 01 2008 01 2010 Table presents the original series with forecasts and forecast error th
137. to the software The current version of Demetra 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 So the results can be more easily compared This implies that many diagnostics statistics auxiliary results etc are computed outside the core engines Demetrat 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 different statistical algorithmic choices possible bugs In any case the global messages on a 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 Demetra 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 Wien
138. ts of the regression variables in the state vector iterative gls model More precisely we consider the following state space model Y Z a a a B Z Z X a T 0 a RE 0 1 0 where the tildes indicates the matrices of the ARIMA part DEMETRA User Manual doc 127 DEMETRA User Manual In such a model outliers have to be handled carefully indeed for each period corresponding to an outlier the forecast error is missing it cannot be estimated the same way that initial residuals cannot be estimated when the model contains regression variables like calendar effects 1 4 Final remarks It should be noted that the original solution of Tramo 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 Finally below we give a summary of the characteristics of the different solutions considering the degrees of freedom of the residuals and their respect of the time structure interpretation of the residuals in the time domain Number of Independence of the Respect of the time residuals residuals structure Tramo OR residuais m k fF Tramo ullresiduals n Sd pa T a S partial Bemer n o o S oo 2 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 X
139. window X12 or TramoSeats can be dragged and dropped with the mouse to any other window of the Tools menu It is also possible to drag and drop the results in the item chosen from container DEMETRA User Manual doc 27 o anh co ho BSSSSSSSRRe a DEMETRA User Manual De B 10 x Source XCLPRVDR Name Industries alimentaires 001563038 jan feb mar apr may jun jul aug sep oct nov d 1990 90 1759 90 531 90 7935 91 0339 91 1342 91 1991 91 727 92 1036 92 3993 92 5969 92 8775 93 0494 93 0101 92 9564 92 8958 92 8929 929923 93 1992 93 1416 93 2938 93 6028 93 7782 93 7544 93 8555 93 9261 93 7982 93 6618 93 4079 93 1276 92 1993 926473 92 365 92 1184 92 036 91 9859 91 9647 92 0916 92 2279 92 3067 92 3454 92 4593 92 994 92 7179 92 9295 92 9943 93 0468 93 2266 93 2663 93 2749 93 4096 93 5665 93 9244 94 0728 94 1995 94 3763 94 472 94 7609 95 1125 95 3431 95 6214 95 8509 95 9689 96 1102 96 2225 96 2902 9 1996 96 7442 97 1059 97 4285 97 6739 97 8944 98 0751 98 2278 98 405 98 526 98 7485 99 0255 99 1997 990784 99 0939 99 0633 99 1356 99 4343 99 7614 100 061 100 201 100 346 100 463 100 447 10 1998 100 7 amp 101 103 101 469 101 634 101 56 101 444 101 325 101 265 101 267 101 128 101 048 10 1999 101 077 Q0 948 100 824 101 008 101 273 101 313 101 314 101274 101 21 101 26 101 382 10 2000 101 18 101899 100 928 10055 100 114 100 06 100 089 100 081 100 123 100 185 100 245 10 2001 100 57 100 608 100 691 100 693 100 694 100 7
140. yss mea 12 n 2 z log y 4 y7 1 Transformation of the kurtosis Wilson Hilferty p S 6 n 3 n 1 n 15n 4 q Ma 2 n 5 n Tn 27n 70 66 DEMETRA User Manual doc 130 DEMETRA User Manual o n 7 nt 5 nt T n 2n 5 p 66 nt 5 nt 7 n 7 n 37n 11n 313 126 A art c s s vy 2 k 1 s7 _ eee a a a a if DH z z 2 4 2 Ljung Box test The Ljung Box test is defined as follows let P the sample autocorrelation at rank j of the n residuals The Ljung Box statistics is LB k n n ny FE If the residuals are random it should be distributed as yv k np where np is the number of hyper parameters of the model from which the residuals are derived 4 3 Spectral test 4 3 1 Definition of the periodogram The periodogram of the series y is computed as follows 1 The y is standardized m pas n 5 Eo D DEMETRA User Manual doc 131 DEMETRA User Manual 2 The periodogram is computed on the standardized z 2 I A 7 Ci D Si A where C A Y cos Ar z and A Y sin Ar z t 1 t 1 4 3 2 Periodogram at the Fourier frequencies The Fourier frequencies are defined by A i o lt js n Z J If the z are iid N 0 1 it is easy to see that the corresponding quantities J A are iid x 2 We have indeed that yet if j k Oif j k t 1 and Y cos 4t Ysin 4 4 7 t 1 t 1 2 2 so tha

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