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

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  • Polasek, Wolfgang

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria and University of 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.

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File URL: http://www.ihs.ac.at/publications/eco/es-277.pdf
File Function: First version, 2011
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Bibliographic Info

Paper provided by Institute for Advanced Studies in its series Economics Series with number 277.

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Length: 19 pages
Date of creation: Nov 2011
Date of revision:
Handle: RePEc:ihs:ihsesp:277

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Related research

Keywords: Hodrick-Prescott (HP) smoothers; Model selection by marginal likelihoods; Multi-normal-gamma distribution; Spatial sales growth data; Bayesian econometrics;

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References

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  1. Wolfgang Polasek, 2011. "MCMC Estimation of Extended Hodrick-Prescott (HP) Filtering Models," Working Paper Series 25_11, The Rimini Centre for Economic Analysis.
  2. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the business cycle: A modified Hodrick-Prescott filter," Spanish Economic Review, Springer, vol. 1(2), pages 175-206.
  3. Robert J. Hodrick & Edward Prescott, 1981. "Post-War U.S. Business Cycles: An Empirical Investigation," Discussion Papers 451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  4. Richard Sellner & Wolfgang Polasek, 2011. "Does Globalization a ffect Regional Growth? Evidence for NUTS-2 Regions in EU-27," ERSA conference papers ersa11p819, European Regional Science Association.
  5. Morten O. Ravn & Harald Uhlig, 2001. "On Adjusting the HP-Filter for the Frequency of Observations," CESifo Working Paper Series 479, CESifo Group Munich.
  6. 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.
  7. 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.
  8. 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.
  9. Polasek, Wolfgang, 2011. "The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model," Economics Series 277, Institute for Advanced Studies.
  10. 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.
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Cited by:
  1. Polasek, Wolfgang, 2011. "The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model," Economics Series 277, Institute for Advanced Studies.
  2. 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.

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