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

Wolfgang Polasek

No 277, Economics Series from Institute for Advanced Studies

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.

Keywords: Hodrick-Prescott (HP) smoothers; Model selection by marginal likelihoods; Multi-normal-gamma distribution; Spatial sales growth data; Bayesian econometrics (search for similar items in EconPapers)
JEL-codes: C11 C15 C52 E17 R12 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2011-11
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (2)

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https://irihs.ihs.ac.at/id/eprint/2096 First version, 2011 (application/pdf)

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Working Paper: The Hodrick-Prescott (HP) Filter as a Bayesian Regression Model (2012)
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