The Hodrick-Prescott (HP) filter as a Bayesian regression model

Arbeitspapier

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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: Reihe Ökonomie / Economics Series ; No. 277

Classification and Topics

• Classification: Wirtschaft ; Bayesian Analysis: General ; Statistical Simulation Methods: General ; Model Evaluation, Validation, and Selection ; General Aggregative Models: Forecasting and Simulation: Models and Applications ; Size and Spatial Distributions of Regional Economic Activity
• Subject: Hodrick-Prescott (HP) smoothers ; model selection by marginal likelihoods ; multi-normalgamma distribution ; Spatial sales growth data ; Bayesian econometrics

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Polasek, Wolfgang
• Event: Veröffentlichung
• (who): Institute for Advanced Studies (IHS)
• (where): Vienna
• (when): 2011

Further information

• Handle: http://hdl.handle.net/10419/68522
• Last update: 10.03.2025, 11:41 AM CET