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Three Equivalent Methods for Filtering Finite Nonstationary Time Series

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  • Gomez, Victor

Abstract

To estimate the components in an unobserved autoregressive integrated moving average components model, three different approaches can be used--Kalman filtering plus smoothing, Wiener-Kolmogorov filtering, and penalized least squares smoothing. It is shown, in the article, that the three approaches are equivalent. As an application, it is shown that any of the three approaches can be used to filter a series with the Hodrick-Prescott filter but that Wiener-Kolmogorov filtering should be recommended.

Suggested Citation

  • Gomez, Victor, 1999. "Three Equivalent Methods for Filtering Finite Nonstationary Time Series," Journal of Business & Economic Statistics, American Statistical Association, vol. 17(1), pages 109-116, January.
    • Handle: RePEc:bes:jnlbes:v:17:y:1999:i:1:p:109-16
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    Cited by:

    1. Kum Hwa Oh & Eric Zivot & Drew Creal, 2006. "The Relationship between the Beveridge-Nelson Decomposition andUnobserved Component Models with Correlated Shocks," Working Papers UWEC-2006-16-FC, University of Washington, Department of Economics.
    2. Regina Kaiser & Agustín Maravall, 2002. "A Complete Model-Based Interpretation of the Hodrick-Prescott Filter: Spuriousness Reconsidered," Working Papers 0208, Banco de España.
    3. Canova, Fabio, 2014. "Bridging DSGE models and the raw data," Journal of Monetary Economics, Elsevier, vol. 67(C), pages 1-15.
    4. Drew Creal & Siem Jan Koopman & Eric Zivot, 2010. "Extracting a robust US business cycle using a time-varying multivariate model-based bandpass filter," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 25(4), pages 695-719.
    5. repec:ehl:lserod:56407 is not listed on IDEAS
    6. 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.
    7. Flaig Gebhard, 2015. "Why We Should Use High Values for the Smoothing Parameter of the Hodrick-Prescott Filter," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), De Gruyter, vol. 235(6), pages 518-538, December.
    8. Pollock, D. S. G., 2003. "Improved frequency selective filters," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 279-297, March.
    9. Kristian Jönsson, 2018. "Extending the state-space representation of the judgement-augmented Hodrick-Prescott filter," Economics Bulletin, AccessEcon, vol. 38(1), pages 623-628.
    10. Oh, Kum Hwa & Zivot, Eric & Creal, Drew, 2008. "The relationship between the Beveridge-Nelson decomposition and other permanent-transitory decompositions that are popular in economics," Journal of Econometrics, Elsevier, vol. 146(2), pages 207-219, October.
    11. Michal Andrle, 2013. "What Is in Your Output Gap? Unified Framework & Decomposition into Observables," IMF Working Papers 2013/105, International Monetary Fund.
    12. Rafael Doménech & Víctor Gómez, 2005. "Ciclo económico y desempleo estructural en la economía española," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 259-288, May.
    13. Gerba, Eddie, 2015. "Have the US macro-financial linkages changed? The balance sheet dimension," LSE Research Online Documents on Economics 59886, London School of Economics and Political Science, LSE Library.
    14. Jaqueson K. Galimberti & Marcelo L. Moura, 2011. "Improving the reliability of real-time Hodrick-Prescott filtering using survey forecasts," Centre for Growth and Business Cycle Research Discussion Paper Series 159, Economics, The University of Manchester.
    15. Ombao, Hernando & Ringo Ho, Moon-ho, 2006. "Time-dependent frequency domain principal components analysis of multichannel non-stationary signals," Computational Statistics & Data Analysis, Elsevier, vol. 50(9), pages 2339-2360, May.
    16. Regina Kaiser & Agustín Maravall, 2000. "Notes on Time Series Analysis, ARIMA Models and Signal Extraction," Working Papers 0012, Banco de España.
    17. Pollock, D. S. G., 2003. "Improved frequency selective filters," Computational Statistics & Data Analysis, Elsevier, vol. 42(3), pages 279-297, March.

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