IDEAS home Printed from https://ideas.repec.org/a/spr/series/v7y2016i1d10.1007_s13209-015-0137-y.html
   My bibliography  Save this article

On some remarks about SEATS signal extraction

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s13209-015-0137-y
    File Function: Abstract
    Download Restriction: no
    File URL: https://libkey.io/10.1007/s13209-015-0137-y?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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.
    3. Findley, David F, et al, 1998. "New Capabilities and Methods of the X-12-ARIMA Seasonal-Adjustment Program," Journal of Business & Economic Statistics, American Statistical Association, vol. 16(2), pages 127-152, April.
    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.
    7. Maravall, Agustin & Planas, Christophe, 1999. "Estimation error and the specification of unobserved component models," Journal of Econometrics, Elsevier, vol. 92(2), pages 325-353, October.
    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.
    9. McElroy, Tucker, 2008. "Matrix Formulas For Nonstationary Arima Signal Extraction," Econometric Theory, Cambridge University Press, vol. 24(4), pages 988-1009, August.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Kirchner, Robert, 1999. "Auswirkungen des neuen Saisonbereinigungsverfahrens Census X-12-ARIMA auf die aktuelle Wirtschaftsanalyse in Deutschland," Discussion Paper Series 1: Economic Studies 1999,07, Deutsche Bundesbank.
    2. Viv B. Hall & Peter Thomson, 2021. "Does Hamilton’s OLS Regression Provide a “better alternative” to the Hodrick-Prescott Filter? A New Zealand Business Cycle Perspective," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 17(2), pages 151-183, November.
    3. Maravall, Agustin, 2006. "An application of the TRAMO-SEATS automatic procedure; direct versus indirect adjustment," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2167-2190, May.
    4. Thornton, Michael A., 2013. "Removing seasonality under a changing regime: Filtering new car sales," Computational Statistics & Data Analysis, Elsevier, vol. 58(C), pages 4-14.
    5. McElroy, Tucker & Wildi, Marc, 2013. "Multi-step-ahead estimation of time series models," International Journal of Forecasting, Elsevier, vol. 29(3), pages 378-394.
    6. Maravall, Agustín, 2000. "Notes on time serie analysis, ARIMA models and signal extraction," DES - Working Papers. Statistics and Econometrics. WS 10058, Universidad Carlos III de Madrid. Departamento de Estadística.
    7. McElroy, Tucker S. & Jach, Agnieszka, 2023. "Identification of the differencing operator of a non-stationary time series via testing for zeroes in the spectral density," Computational Statistics & Data Analysis, Elsevier, vol. 177(C).
    8. Víctor M. Guerrero & Adriana Galicia‐Vázquez, 2010. "Trend estimation of financial time series," Applied Stochastic Models in Business and Industry, John Wiley & Sons, vol. 26(3), pages 205-223, May.
    9. De Gooijer, Jan G. & Hyndman, Rob J., 2006. "25 years of time series forecasting," International Journal of Forecasting, Elsevier, vol. 22(3), pages 443-473.
    10. Viv B Hall & Peter Thomson, 2020. "Does Hamilton’s OLS regression provide a “better alternative†to the Hodrick-Prescott filter? A New Zealand business cycle perspective," CAMA Working Papers 2020-71, Centre for Applied Macroeconomic Analysis, Crawford School of Public Policy, The Australian National University.
    11. McElroy Tucker S, 2010. "A Nonlinear Algorithm for Seasonal Adjustment in Multiplicative Component Decompositions," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 14(4), pages 1-23, September.
    12. Maravall, A. & del Rio, A., 2007. "Temporal aggregation, systematic sampling, and the Hodrick-Prescott filter," Computational Statistics & Data Analysis, Elsevier, vol. 52(2), pages 975-998, October.
    13. Mauricio Gallardo & Hernán Rubio, 2009. "Diagnóstico de estacionalidad con X-12-ARIMA," Economic Statistics Series 76, Central Bank of Chile.
    14. Kroes, James R. & Manikas, Andrew S. & Gattiker, Thomas F., 2018. "Operational leanness and retail firm performance since 1980," International Journal of Production Economics, Elsevier, vol. 197(C), pages 262-274.
    15. Quenneville, Benoit & Ladiray, Dominique & Lefrancois, Bernard, 2003. "A note on Musgrave asymmetrical trend-cycle filters," International Journal of Forecasting, Elsevier, vol. 19(4), pages 727-734.
    16. Massmann, Michael & Mitchell, James, 2003. "Reconsidering the evidence: Are Eurozone business cycles converging," ZEI Working Papers B 05-2003, University of Bonn, ZEI - Center for European Integration Studies.
    17. Regina Kaiser & Agustín Maravall, 2000. "Notes on Time Series Analysis, ARIMA Models and Signal Extraction," Working Papers 0012, Banco de España.
    18. Hai Yue Liu & Xiao Lan Chen, 2017. "The imported price, inflation and exchange rate pass-through in China," Cogent Economics & Finance, Taylor & Francis Journals, vol. 5(1), pages 1279814-127, January.
    19. Carlos A. Medel, 2018. "A Comparison Between Direct and Indirect Seasonal Adjustment of the Chilean GDP 1986–2009 with X-12-ARIMA," Journal of Business Cycle Research, Springer;Centre for International Research on Economic Tendency Surveys (CIRET), vol. 14(1), pages 47-87, April.
    20. Stefania D'Amico & Athanasios Orphanides, 2008. "Uncertainty and disagreement in economic forecasting," Finance and Economics Discussion Series 2008-56, Board of Governors of the Federal Reserve System (U.S.).

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:series:v:7:y:2016:i:1:d:10.1007_s13209-015-0137-y. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.