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Detrending economic time series: a Bayesian generalization of the Hodrick-Prescott filter

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  • Thomas M. Trimbur

    (Faculty of Economics, Cambridge University, UK)

Abstract

This article develops a new method for detrending time series. It is shown how, in a Bayesian framework, a generalized version of the Hodrick-Prescott filter is obtained by specifying prior densities on the signal-to-noise ratio (q) in the underlying unobserved components model. This helps ensure an appropriate degree of smoothness in the estimated trend while allowing for uncertainty in q. The article discusses the important issue of prior elicitation for time series recorded at different frequencies. By combining prior expectations with the likelihood, the Bayesian approach permits detrending in a way that is more consistent with the properties of the series. The method is illustrated with some quarterly and annual US macroeconomic series. Copyright © 2006 John Wiley & Sons, Ltd.

Suggested Citation

  • Thomas M. Trimbur, 2006. "Detrending economic time series: a Bayesian generalization of the Hodrick-Prescott filter," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 25(4), pages 247-273.
    • Handle: RePEc:jof:jforec:v:25:y:2006:i:4:p:247-273
    DOI: 10.1002/for.987
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    Cited by:

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    2. Dermoune Azzouz & Djehiche Boualem & Rahmania Nadji, 2009. "Multivariate Extension of the Hodrick-Prescott Filter-Optimality and Characterization," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(3), pages 1-35, May.
    3. Kauermann Goeran & Krivobokova Tatyana & Semmler Willi, 2011. "Filtering Time Series with Penalized Splines," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 15(2), pages 1-28, March.
    4. Álvarez, Luis J. & Gómez-Loscos, Ana, 2018. "A menu on output gap estimation methods," Journal of Policy Modeling, Elsevier, vol. 40(4), pages 827-850.
    5. Ferroni Filippo, 2011. "Trend Agnostic One-Step Estimation of DSGE Models," The B.E. Journal of Macroeconomics, De Gruyter, vol. 11(1), pages 1-36, July.
    6. Rodrigo Barbone Gonzalez & Joaquim Lima & Leonardo Marinho, 2015. "Countercyclical Capital Buffers: bayesian estimates and alternatives focusing on credit growth," Working Papers Series 384, Central Bank of Brazil, Research Department.
    7. Miroslav Plašil, 2011. "Potenciální produkt, mezera výstupu a míra nejistoty spojená s jejich určením při použití Hodrick-Prescottova filtru [Potential Product, Output Gap and Uncertainty Rate Associated with Their Determ," Politická ekonomie, Prague University of Economics and Business, vol. 2011(4), pages 490-507.

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