IDEAS home Printed from https://ideas.repec.org/p/ihs/ihsesp/277.html
   My bibliography  Save this paper

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

Author

Listed:
  • 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.

Suggested Citation

  • Polasek, Wolfgang, 2011. "The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model," Economics Series 277, Institute for Advanced Studies.
  • Handle: RePEc:ihs:ihsesp:277
    as

    Download full text from publisher

    File URL: http://www.ihs.ac.at/publications/eco/es-277.pdf
    File Function: First version, 2011
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Polasek, Wolfgang, 2011. "The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model," Economics Series 277, Institute for Advanced Studies.
    2. Richard Sellner & Wolfgang Polasek, 2011. "Does Globalization affect Regional Growth? Evidence for NUTS-2 Regions in EU-27," ERSA conference papers ersa11p819, European Regional Science Association.
    3. 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.
    4. 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.
    5. 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.
    6. 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.
    7. 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.
    8. 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.
    9. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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.

    More about this item

    Keywords

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

    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)

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:ihs:ihsesp:277. 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: (Doris Szoncsitz). General contact details of provider: http://edirc.repec.org/data/deihsat.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.