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A Prototypical Seasonal Adjustment Model

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  • Agustin Maravall
  • David A. Pierce

Abstract

. The paper analyses unobserved‐components modelling and estimation for the simplest ARIMA process that accepts a full decomposition into trend, seasonal and irregular components. This prototypical model exemplifies many features of and issues arising in model‐based seasonal adjustment that are less transparent in more complex seasonal time series models. In particular the analysis illuminates the major issues surrounding the specification of the component models and the identification of a unique structure for them. In so doing, the relationship between reduced‐ and structural‐form approaches to unobserved components estimation is illustrated within an ARIMA‐modelling framework. Finally, the properties of the minimum mean‐squared‐error estimators of the unobserved components are examined and the two main types of estimation error, revisions in the preliminary estimator and error in the final estimator, are analysed.

Suggested Citation

  • Agustin Maravall & David A. Pierce, 1987. "A Prototypical Seasonal Adjustment Model," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 177-193, March.
    • Handle: RePEc:bla:jtsera:v:8:y:1987:i:2:p:177-193
    DOI: 10.1111/j.1467-9892.1987.tb00431.x
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    Cited by:

    1. Victor Gomez & Jorg Breitung, 1999. "The Beveridge–Nelson Decomposition: A Different Perspective with New Results," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 527-535, September.
    2. David F. Findley & Demetra P. Lytras & Agustin Maravall, 2016. "Illuminating ARIMA model-based seasonal adjustment with three fundamental seasonal models," SERIEs: Journal of the Spanish Economic Association, Springer;Spanish Economic Association, vol. 7(1), pages 11-52, March.
    3. del Barrio Castro, Tomas & Pons Fanals, Ernest & Surinach Caralt, Jordi, 2002. "The effects of working with seasonally adjusted data when testing for unit root," Economics Letters, Elsevier, vol. 75(2), pages 249-256, April.
    4. F. Javier TRIVEZ & Angel Mauricio REYES & F. Javier ALIAGA, 2009. "MEXICAN MAQUILA INDUSTRY OUTLOOK. A Quantitative Space-Time Analysis," Regional and Sectoral Economic Studies, Euro-American Association of Economic Development, vol. 9(1).
    5. Stephen Pollock, 2001. "Signal Extraction, Maximum Likelihood Estimation and the Start-up Problem," Working Papers 433, Queen Mary University of London, School of Economics and Finance.
    6. Gianluca Caporello & Agustín Maravall & Fernando J. Sánchez, 2001. "Program TSW Reference Manual," Working Papers 0112, Banco de España.
    7. 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.
    8. Stephen Pollock, 2005. "Econometric Methods of Signal Extraction," Working Papers 530, Queen Mary University of London, School of Economics and Finance.
    9. Stephen Pollock, 2001. "Signal Extraction, Maximum Likelihood Estimation and the Start-up Problem," Working Papers 433, Queen Mary University of London, School of Economics and Finance.
    10. Michael Fung, 2013. "A trade-off between non-fundamental risk and incentives," Review of Quantitative Finance and Accounting, Springer, vol. 41(1), pages 29-51, July.
    11. Pollock, D. S. G., 2001. "Methodology for trend estimation," Economic Modelling, Elsevier, vol. 18(1), pages 75-96, January.
    12. Breitung, Jörg, 1998. "On model based seasonal adjustment procedures," SFB 373 Discussion Papers 1998,12, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    13. Thury, Gerhard & Witt, Stephen F., 1998. "Forecasting industrial production using structural time series models," Omega, Elsevier, vol. 26(6), pages 751-767, December.
    14. Pollock Stephen D.S.G., 2009. "Statistical Fourier Analysis: Clarifications and Interpretations," Journal of Time Series Econometrics, De Gruyter, vol. 1(1), pages 1-49, April.
    15. Fok, D. & Franses, Ph.H.B.F. & Paap, R., 2005. "Performance of Seasonal Adjustment Procedures: Simulation and Empirical Results," Econometric Institute Research Papers EI 2005-30, Erasmus University Rotterdam, Erasmus School of Economics (ESE), Econometric Institute.
    16. Pollock, D.S.G., 2006. "Econometric methods of signal extraction," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2268-2292, May.
    17. 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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