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Estimation Error and the Specification of Unobserved Component Models

Author

Listed:
  • Agustín Maravall
  • Cristophe Planas

Abstract

The paper deals with the problem of identifying stochastic unobserved two-component models, as in seasonal adjustment or trend-cycle decompositions. Solutions based on the properties of the unobserved component estimation error are considered, and analytical expressions for the variances and covariances of the different types of estimation errors (errors in the final, preliminary, and concurrent estimator and in the forecast) are obtained for any admissible decomposition.

Suggested Citation

  • Agustín Maravall & Cristophe Planas, 1996. "Estimation Error and the Specification of Unobserved Component Models," Working Papers 9608, Banco de España.
    • Handle: RePEc:bde:wpaper:9608
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    References listed on IDEAS

    as
    1. Stock, James H & Watson, Mark W, 1988. "Variable Trends in Economic Time Series," Journal of Economic Perspectives, American Economic Association, vol. 2(3), pages 147-174, Summer.
    2. Arnold Zellner, 1978. "Seasonal Analysis of Economic Time Series," NBER Books, National Bureau of Economic Research, Inc, number zell78-1.
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    4. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Time Series: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 343-349, October.
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    6. Bell, William R & Hillmer, Steven C, 1984. "Issues Involved with the Seasonal Adjustment of Economic Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 2(4), pages 291-320, October.
    7. Maravall, Agustin & Mathis, Alexandre, 1994. "Encompassing univariate models in multivariate time series : A case study," Journal of Econometrics, Elsevier, vol. 61(2), pages 197-233, April.
    8. David A. Pierce, 1978. "Seasonal Adjustment When Both Deterministic and Stochastic Seasonality Are Present," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 242-280, National Bureau of Economic Research, Inc.
    9. Pierce, David A., 1980. "Data revisions with moving average seasonal adjustment procedures," Journal of Econometrics, Elsevier, vol. 14(1), pages 95-114, September.
    10. George E. P. Box & Steven C. Hillmer & George C. Tiao, 1978. "Analysis and Modeling of Seasonal Time Series," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 309-344, National Bureau of Economic Research, Inc.
    11. Harvey, A C & Todd, P H J, 1983. "Forecasting Economic Time Series with Structural and Box-Jenkins Models: A Case Study," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(4), pages 299-307, October.
    12. Harvey, A C & Todd, P H J, 1983. "Forecasting Economic Time Series with Structural and Box-Jenkins Models: A Case Study: Response," Journal of Business & Economic Statistics, American Statistical Association, vol. 1(4), pages 313-315, October.
    13. David A. Pierce, 1978. "Seasonal adjustment when both deterministic and stochastic seasonality are present," Special Studies Papers 107, Board of Governors of the Federal Reserve System (U.S.).
    14. Agustín Maravall, 1996. "Unobserved Components in Economic Time Series," Working Papers 9609, Banco de España.
    15. Robert F. Engle, 1978. "Estimating Structural Models of Seasonality," NBER Chapters, in: Seasonal Analysis of Economic Time Series, pages 281-308, National Bureau of Economic Research, Inc.
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    Cited by:

    1. Laurent Ferrara & Dominique Guégan, 2006. "Detection of the Industrial Business Cycle using SETAR Models," Journal of Business Cycle Measurement and Analysis, OECD Publishing, Centre for International Research on Economic Tendency Surveys, vol. 2005(3), pages 353-371.
    2. Tommaso Proietti, 2021. "Predictability, real time estimation, and the formulation of unobserved components models," Econometric Reviews, Taylor & Francis Journals, vol. 40(5), pages 433-454, April.
    3. Norman Loayza & Klaus Schmidt-Hebbel & Luis Servén, 2000. "What Drives Private Saving Across the World?," The Review of Economics and Statistics, MIT Press, vol. 82(2), pages 165-181, May.
    4. 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.
    5. Regina Kaiser & Agustín Maravall, 2000. "Notes on Time Series Analysis, ARIMA Models and Signal Extraction," Working Papers 0012, Banco de España.
    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. Rossi, Alessandro & Gallo, Giampiero M., 2006. "Volatility estimation via hidden Markov models," Journal of Empirical Finance, Elsevier, vol. 13(2), pages 203-230, March.
    8. 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.
    9. Kaloyan Ganev, 2004. "Statistical estimates of the deviations from the macroeconomic potential. An application to the economy of Bulgaria," Macroeconomics 0409010, University Library of Munich, Germany.
    10. Loayza, Norman & Schmidt-Hebbel, Klaus & Serven, Luis, 2000. "What drives private saving around the world?," Policy Research Working Paper Series 2309, The World Bank.
    11. Gianluca Caporello & Agustín Maravall & Fernando J. Sánchez, 2001. "Program TSW Reference Manual," Working Papers 0112, Banco de España.
    12. Daragh Clancy, 2013. "Output Gap Estimation Uncertainty: Extracting the TFP Cycle Using an Aggregated PMI Series," The Economic and Social Review, Economic and Social Studies, vol. 44(1), pages 1-18.

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    More about this item

    Keywords

    EVALUATION; ECONOMETRICS; MODELS;
    All these keywords.

    JEL classification:

    • C10 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - General
    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C19 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Other

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