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Programs Tramo (Time Series Regression with Arima Noise PROGRAMS TRAMO (TIME SERIES REGRESSION WITH ARIMA NOISE, MISSING OBSERVATIONS AND OUTLIERS) AND SEATS (SIGNALEXTRACTIONS AREMA TIME SERIES) INSTRUCTIONS FOR THE USER (BETA VERSION: JUNIO 1997) Víctor Gómez * Agustín Maravall ** SGAPE-97001 Julio 1997 * Ministerio de Economía y Hacienda ** Banco de España This software is available at the following Internet address: http://www.bde.es The Working Papers of the Dirección General de Análisis y Programación Presupuestaria are not official statements of the Ministerio de Economía y Hacienda Abstract Brief summaries and user Instructions are presented for the programs-* TRAMO ("Time 'Series Regression with ARTMA Noise, Missing Observations and Outliers") and SEATS ("Signal Extraction in ARIMA Time Series"). TRAMO is a program for estimation and forecasting of regression models with possibly nonstationary (ARIMA) errors and any sequence of missing val- ues. The program interpolates these values, identifies and corrects for several types of outliers, and estimates special effects such as Trading Day and Easter and, in general, intervention variable type of effects. Fully automatic model identification and outlier correction procedures are available. SEATS is a program for estimation of unobserved components in time se- ries following the so-called ARlMA-model-based method. The trend, seasonal, irregular, and cyclical components are estimated and forecasted with signal extraction techniques applied to ARIMA models. The standard errors of the es- timates and forecasts are obtained and the model-based structure is exploited to answer questions of interest in short-term analysis of the data. The two programs are structured so as to be used together both for in- depth analysis of a few series (as presently done at the Bank of Spain) or for automatic routine applications to a large number of series (as presently done at Eurostat). When used for seasonal adjustment, TRAMO preadjusts the series to be adjusted by SEATS. ACKNOWLEDGEMENTS This version of TRAMO and SEATS is the result of roughly eight years of work. During this period many persons have helped in innumerable ways, so that thorough recognition is unfeasible. Special mention, however, must be made. First, there is thevcrucialirole of Gianluca Caporello in the development of- the programs. We have srelied enormously on his commitment, expertise and ^ability regarding any issue related to software development and application. Counting-^on people like Gianluca has only one drawback: it then becomes difficult to imagine life without them. The starting point for SEATS was a program J. Peter Burman had been de- veloping for seasonal adjustment at the Bank of England, and his work contained very nice features. Thus, to the Bank of England, and most particularly to J. Peter Burman for his generous help, we wish to express our gratitude. We should next mention the seven years of research support by the European University Institute, in Florence. Two specific mentions should be made. One con- cerns the very special comments, support, and encouragement afforded by Edmond Malinvaud and Paul Champsaur, the members of Research Council that monitored the research. The second mention goes to the generous help of several doctoral stu- dents; two of them, Christophe Planas and Gabriele Fiorentini, should be recognized. Last, but certainly not least, thanks are due to the excellent administrative work of Barbara Bonke. We also express our gratitude for the institutional support of Eurostat, with which the programs are now closely linked (many thousand times a month). We have deeply appreciated how a large bureaucracy with a huge task can nevertheless be open to new ideas and have the courage to develop them and challenge inertia and routine. We give special thanks to Berthold Feldmann, Bjórn Fischer and Jens Dossé. Their careful work on large scale applications of TRAMO and SEATS has been invaluable. We wish to thank the Bank of Spain for its current support and the willingness of many economists in the Research Department to apply and experiment with the programs in their work. Two well-deserved mentions are for Juan Carlos Delrieu and Alberto Cabrero. We also thank the computer assistance of Mercedes Sanz, the research assistance of Fernando Sánchez, and the administrative assistance of Isabel de Bias. Finally, some names must be added to the list of acknowledgments: Gerhard Thury and Dieter Proske, Bank of Austria; Marco Bianchi, Bank of England; Roberto Sabbatini and Dario Focarelli, Bank of Italy; Dominique Ladiray, INSEE; Eric Ghysels, University of Montreal; Antoni Espasa, Regina Kaiser, and Daniel Peña, Universi- dad Carlos III; Albert Prat and Manuel Martí-Recover, Universidad Politécnica de Cataluña; Domenico Piccolo, Universitá di Napoli; Pilar Bengoechea, Ministerio de Industria; David Taguas, M- Dolores García Martos and Ángel Sánchez, Ministerio de Economía y Hacienda; and most certainly, we have benefited from the many fruit- ful discussions with Andrew Harvey, London School of Economics, and with David Findley, U.S. Bureau of the Census. 11 Contents 1 Program Tramo I 1.1 Brief Description of the Program 1 1.2 Instructions for the User . 6 1.2.1 Hardware Requirements ... 6 1.2.2 Expanded Memory Manager Vs. Microway Kernel... ... 6 1.2.3 Installation 8 1.2.4 Execution of the Program 9 1.2.5 Command-Line Options 9 1.2.6 Output File 11 1.2.7 Graphics 11 1.2.8 Printing TRAMO User's Manual 11 1.2.9 Downloading TRAMO Using FTP Anonymous 12 1.3 Description of the Input Parameters 13 1.3.1 Control of the Output File 13 1.3.2 ARIMA Model 13 1.3.3 Minimum Number of Observations 14 1.3.4 Pretest for the log vs. level specification 15 1.3.5 Automatic Model Identification 15 1.3.6 Estimation 17 1.3.7 Forecasting 19 1.3.8 Missing Observations 20 1.3.9 Outliers 21 1.3.10 Regression 23 1.3.11 Others 27 1.3.12 Memory Constraints 28 1.4 Input File and Examples . 29 1.5 The File 'Seats.itr' 48 1.6 Identification of the Arrays Produced by TRAMO 54 1.6.1 Series 54 1.6.2 Autocorrelation Functions 54 1.6.3 Regression, Outliers, and Special Effects 55 iii 2 Program Seats 57 2.1 Brief Description of the Program 57 2.2 Decomposition of the ARIMA Model 63 2.3 Instructions for the User . 67 2.4 Description of the Input Parameters . ..-.. .......... 67 2.4.1 Allocation of Regression Effects . .... .67 2.4.2 Specification of the ARIMA Model . 68 2.4.3 Estimation of the ARIMA Model 70 2.4.4 Forecasts and Signal Extraction 71 2.4.5 Bias Correction 71 2.4.6 Cyclical Component 72 2.4.7 Smoothing of the Trend; Use of SEATS as a "Fixed Filter" 73 2.4.8 Other Parameters 74 2.5 Output File 75 2.6 Input File and Examples 77 2.7 Identification of the Arrays Produced by SEATS 88 2.7.1 Series 88 2.7.2 Autocorrelation Functions 90 2.7.3 Spectra 90 2.7.4 Filters 91 2.7.5 Forecasts 91 3 Routine use on Many Series 93 3.1 The RSA Parameter 93 3.2 The ITER Parameter 99 3.3 An Application 116 4 References 119 5 Classification of Input Parameters by Function 123 5.1 Program Tramo 123 5.2 Program Seats 125 5.3 Routine Use on Many Series 126 Index 127 IV 1 Program Tramo 1.1 Brief Description of the Program TRAMO ("Time Series Regression with ARIMA Noise, Missing Observations, and Outliers") is a program written in Fortran for mainframes and PCs under MS—Dos; The program performs estimation, forecasting, and interpolation of regression models with missing observations and ARIMA errors, in the presence of possibly several types of outliers. The ARIMA model can be identified auto- matically. (No restriction is imposed on the location of the missing observations in the series.) Given the vector of observations: z=(ztl,...,ztM] (1) where 0 < t\ < ... < ÍM, the program fits the regression model zt = y'tp + vt, (2) where /3 = (/?i,..., /3n)' is a vector of regression coefficients, y't = (yu,..., ynt) denotes n regression variables, and vt follows the general ARIMA process <f>(B) 6(B) Vi = 9(B) at, (3) where B is the backshift operator; (f>(B), ¿(B), and 0(B) are finite polynomials in B, and at is assumed a n.i.i.d. (0,<r^) white-noise innovation. The polynomial S(B] contains the unit roots associated with differencing (regular and seasonal), <j)(B) is the polynomial with the stationary autoregres- sive roots (and the complex unit roots, if present), and 6(B) denotes the (in- vertible) moving average polynomial. In TRAMO, they assume the following multiplicative form: S(B) = (I - Bf (I - BS}D p </>(B) = (! + <!>1B + ... + <f>pB*)(l + $lB' + ... + $pB'* ) 1 s s Q 9(B) = (l + 6lB + ... + 9qB' )(l + QiB + ... + QQB * ), where s denotes the number of observations per year. The model may contain a constant //, equal to the mean of the differenced series 8(B)zp In practice, this parameter is estimated as one of the regression parameters in (2). As explained in Section 1.3, initial estimates of the parameters can be input by the user, set to the default values, or computed by the program. The regression variables can be input by the user (such as economic vari- ables thought to be related with zt), or generated by the program. The variables that can be generated are trading day, easter effect and intervention variables of the type: 1 a) dummy variables (additive outliers); b) any possible sequence of ones and zeros; c) 1/(1 — SB) of any sequence of ones and zeros, where 0 < 6 < 1; S d) 1/(1 — 6SB ) of any sequence of ones and zeros, where 0 < 6S < 1; e) 1/(1 — J3) (1 — £?s) of any sequence of ones and zeros.
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