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On some remarks about SEATS signal extraction

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  • Guy Mélard

    (ECARES, Université libre de Bruxelles (U.L.B.) and ITSE)

Abstract

In seasonal adjustment a time series is considered as a juxtaposition of several components, the trend-cycle, and the seasonal and irregular components. The Bureau of the Census X-11 method, based on moving averages, correction of large errors and trading day adjustments, has long dominated. With the success of ARIMA modelling at the end of the 20th century, methods with better outlier detection and trading day corrections by regression with ARIMA errors have appeared, with the regARIMA module of Census X-12-ARIMA or Bank of Spain TRAMO-SEATS. SEATS consists of extracting the components by an ARIMA-model-based unobserved components approach. This means that models are used for each component such that the sum of the components is compatible with the ARIMA model for the corrected time series. The underlying theory of the SEATS program is studied in many papers but there is no complete and systematic description of its output. Our purpose is to examine SEATS text output and to explain the results in simple words and formulas. This is done on a simple example, a time series with a non-seasonal model so that the computations can be verified step by step. The principles behind SEATS are first described, including the admissible decompositions and the canonical decomposition, and the derivation of the Wiener-Kolmogorov filter. Then the example is introduced: the interest rates of US certificates of deposits. The text output from SEATS is presented in edited form in several tables. Finally, the main results are checked on the example by means of a Microsoft Excel workbook and direct computations. In particular, the forecasts and backcasts are obtained; the admissible and canonical decompositions with two components are discussed; the filters are first derived using autocorrelations of two auxiliary ARMA processes, then applied on the prolonged time series; and the characteristics of the estimates, the revisions and the growth rates are analyzed.

Suggested Citation

  • Guy Mélard, 2016. "On some remarks about SEATS signal extraction," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 53-98, March.
    • Handle: RePEc:spr:series:v:7:y:2016:i:1:d:10.1007_s13209-015-0137-y
    DOI: 10.1007/s13209-015-0137-y
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    References listed on IDEAS

    as
    1. Pollock, D.S.G., 2006. "Econometric methods of signal extraction," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2268-2292, May.
    2. Pierce, David A., 1980. "Data revisions with moving average seasonal adjustment procedures," Journal of Econometrics, Elsevier, vol. 14(1), pages 95-114, September.
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    4. Kaiser, Regina & Maravall, Agustin, 2005. "Combining filter design with model-based filtering (with an application to business-cycle estimation)," International Journal of Forecasting, Elsevier, vol. 21(4), pages 691-710.
    5. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 169-177, April.
    6. Fiorentini, Gabriele & Planas, Christophe, 2001. "Overcoming Nonadmissibility in ARIMA-Model-Based Signal Extraction," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(4), pages 455-464, October.
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    8. D. S. G. Pollock, 2002. "A review of TSW: the Windows version of the TRAMO-SEATS program," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(3), pages 291-299.
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    More about this item

    Keywords

    SEATS; Seasonal adjustment; Admissible decomposition; Canonical decomposition; Wiener-Kolmogorov filter;
    All these keywords.

    JEL classification:

    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C82 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Macroeconomic Data; Data Access
    • C87 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Econometric Software

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