The Extended Hodrick-Prescott (HP) Filter for Spatial Regression Smoothing

The Hodrick-Prescott (HP) method is a popular smoothing method for economic time series to get a longterm component of stationary series like growth rates. The new extended HP smoothing model is applied to data-sets with an underlying metric and requires a Bayesian linear regression model with a strong prior based on differencing matrices for the smoothness parameter and a weak prior for the regression part. We define a Bayesian spatial smoothing model with neighbors for each observation and we define a smoothness prior similar to the HP filter in time series. This opens a new approach to model-based smoothers for time series and spatial models based on MCMC. We apply it to the NUTS-2 regions of the European Union for regional GDP and GDP per capita, where the fixed effects are removed by an extended HP smoothing model.