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The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model

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  • Wolfgang Polasek

    (Institute for Advanced Studies, Vienna, Austria; University of Porto, Porto, Portugal)

Abstract

The Hodrick-Prescott (HP) method is a popular smoothing method for economic time series to get a smooth or long-term component of stationary series like growth rates. We show that the HP smoother can be viewed as a Bayesian linear model with a strong prior using differencing matrices for the smoothness component. The HP smoothing approach requires a linear regression model with a Bayesian conjugate multi-normal-gamma distribution. The Bayesian approach also allows to make predictions of the HP smoother on both ends of the time series. Furthermore, we show how Bayes tests can determine the order of smoothness in the HP smoothing model. The extended HP smoothing approach is demonstrated for the non-stationary (textbook) airline passenger time series. Thus, the Bayesian extension of the HP model defines a new class of model-based smoothers for (non-stationary) time series and spatial models.

Suggested Citation

  • Wolfgang Polasek, 2011. "The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model," Working Paper series 46_11, Rimini Centre for Economic Analysis, revised Jan 2012.
    • Handle: RePEc:rim:rimwps:46_11
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    References listed on IDEAS

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    1. Polasek, Wolfgang, 2011. "The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model," Economics Series 277, Institute for Advanced Studies.
    2. Marianne Baxter & Robert G. King, 1999. "Measuring Business Cycles: Approximate Band-Pass Filters For Economic Time Series," The Review of Economics and Statistics, MIT Press, vol. 81(4), pages 575-593, November.
    3. Wolfgang Polasek & Richard Sellner, 2013. "The Does Globalization Affect Regional Growth? Evidence for NUTS-2 Regions in EU-27," DANUBE: Law and Economics Review, European Association Comenius - EACO, issue 1, pages 23-65, March.
    4. Uhlig, H.F.H.V.S. & Ravn, M., 1997. "On Adjusting the H-P Filter for the Frequency of Observations," Discussion Paper 1997-50, Tilburg University, Center for Economic Research.
    5. Hodrick, Robert J & Prescott, Edward C, 1997. "Postwar U.S. Business Cycles: An Empirical Investigation," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 29(1), pages 1-16, February.
    6. Blackburn, Keith & Ravn, Morten O, 1992. "Business Cycles in the United Kingdom: Facts and Fictions," Economica, London School of Economics and Political Science, vol. 59(236), pages 383-401, November.
    7. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the business cycle: A modified Hodrick-Prescott filter," Spanish Economic Review, Springer;Spanish Economic Association, vol. 1(2), pages 175-206.
    8. Wolfgang Polasek, 2012. "MCMC Estimation of Extended Hodrick-Prescott (HP) Filtering Models," DANUBE: Law and Economics Review, European Association Comenius - EACO, issue 1, pages 25-52, March.
    9. Ravn, Morten O., 1997. "International business cycles in theory and in practice," Journal of International Money and Finance, Elsevier, vol. 16(2), pages 255-283, April.
    10. King, Robert G. & Rebelo, Sergio T., 1993. "Low frequency filtering and real business cycles," Journal of Economic Dynamics and Control, Elsevier, vol. 17(1-2), pages 207-231.
    11. Finn E. Kydland & Edward C. Prescott, 1990. "Business cycles: real facts and a monetary myth," Quarterly Review, Federal Reserve Bank of Minneapolis, vol. 14(Spr), pages 3-18.
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    Cited by:

    1. David E. Giles, 2013. "Constructing confidence bands for the Hodrick--Prescott filter," Applied Economics Letters, Taylor & Francis Journals, vol. 20(5), pages 480-484, March.
    2. Wolfgang Polasek, 2011. "The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model," Working Paper series 46_11, Rimini Centre for Economic Analysis, revised Jan 2012.

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    More about this item

    Keywords

    Hodrick-Prescott (HP) smoothers; model selection by marginal likelihoods; multi-normal-gamma distribution; Spatial sales growth data; Bayesian econometrics;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • E17 - Macroeconomics and Monetary Economics - - General Aggregative Models - - - Forecasting and Simulation: Models and Applications
    • R12 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - General Regional Economics - - - Size and Spatial Distributions of Regional Economic Activity; Interregional Trade (economic geography)

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