Effects of the Hodrick-Prescott filter on trend and difference stationary time series: implications for business cycle research

This paper studies the effects of applying the Hodrick-Prescott filter to trend and difference stationary time series. Applying the Hodrick-Prescott filter to an integrated process is similar to detrending a random walk. When the data are difference stationary, the Hodrick-Prescott filter can generate business cycle dynamics even if none are present in the original data. We study the implications for interpreting stylized facts about business cycles and for analyzing data generated by real business cycle models.