The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model
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.
|Date of creation:||Nov 2011|
|Date of revision:||Jan 2012|
|Contact details of provider:|| Postal: Via Patara, 3, 47921 Rimini (RN)|
Web page: http://www.rcfea.org
More information through EDIRC
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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).
- Morten O. Ravn & Harald Uhlig, 2001.
"On Adjusting the HP-Filter for the Frequency of Observations,"
CESifo Working Paper Series
479, CESifo Group Munich.
- 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.
- Ravn, Morten O & Uhlig, Harald, 2001. "On Adjusting the HP-Filter for the Frequency of Observations," CEPR Discussion Papers 2858, C.E.P.R. Discussion Papers.
- 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.
- Wolfgang Polasek & Richard Sellner, 2011. "Does Globalization affect Regional Growth? Evidence for NUTS-2 Regions in EU-27," Working Paper Series 24_11, The Rimini Centre for Economic Analysis.
- Polasek, Wolfgang & Sellner, Richard, 2011. "Does Globalization Affect Regional Growth? Evidence for NUTS-2 Regions in EU-27," Economics Series 266, Institute for Advanced Studies.
- Marianne Baxter & Robert G. King, 1995.
"Measuring Business Cycles Approximate Band-Pass Filters for Economic Time Series,"
NBER Working Papers
5022, National Bureau of Economic Research, Inc.
- 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.
- 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.
- Wolfgang Polasek, 2011. "MCMC Estimation of Extended Hodrick-Prescott (HP) Filtering Models," Working Paper Series 25_11, The Rimini Centre for Economic Analysis.
- 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.
- Polasek, Wolfgang, 2011. "The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model," Economics Series 277, Institute for Advanced Studies.
- Robert J. Hodrick & Edward Prescott, 1981.
"Post-War U.S. Business Cycles: An Empirical Investigation,"
451, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
- 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.
- 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.
- Regina Kaiser & Agustín Maravall, 1999. "Estimation of the Business Cycle: a Modified Hodrick-Prescott Filter," Working Papers 9912, Banco de España;Working Papers Homepage.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:rim:rimwps:46_11. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Marco Savioli)
If references are entirely missing, you can add them using this form.