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

  • Polasek, Wolfgang

    (Department of Economics and Finance, Institute for Advanced Studies, Vienna, Austria and University of Porto, Portugal)

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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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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  1. Morten O. Ravn & Harald Uhlig, 2001. "On Adjusting the HP-Filter for the Frequency of Observations," CESifo Working Paper Series 479, CESifo Group Munich.
  2. 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.
  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. Wolfgang Polasek, 2011. "The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model," Working Paper Series 46_11, The Rimini Centre for Economic Analysis, revised Jan 2012.
  5. King, R.G. & Rebelo, S.T., 1989. "Low Frequency Filtering And Real Business Cycles," RCER Working Papers 205, University of Rochester - Center for Economic Research (RCER).
  6. 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.
  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. Wolfgang Polasek, 2011. "MCMC Estimation of Extended Hodrick-Prescott (HP) Filtering Models," Working Paper Series 25_11, The Rimini Centre for Economic Analysis.
  9. 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.
  10. Regina Kaiser & Agustín Maravall, 1999. "Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter," Banco de Espa�a Working Papers 9912, Banco de Espa�a.
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