Why does the trend extracted by the Hodrick-Prescott filtering seem to be more plausible than the linear trend?

摘要

Why does the trend extracted by the Hodrick-Prescott (HP) filtering (HP trend) seem to be more plausible than the linear trend estimated by OLS? This article provides an answer for it. Because the HP filtering is a basic econometric tool, it is necessary to have a precise understanding of the nature of it. This article concludes that the HP trend is calculated by adding the low-frequency component (the long-term periodic fluctuation) of the linearly detrended series to the linear trend, which leads to that the HP trend seems to be more plausible than the linear trend. Other than this key result, this article shows that the HP cycle, which is defined as the residuals of the HP filtering, can be interpreted as the high-frequency component (the short-term periodic fluctuation) of the linearly detrended series. An empirical illustration is also provided.