The Econometrics of the Hodrick-Prescott filter (preliminary)

Mardi | 2013-06-04

Neslihan SAKARYA – Robert DE JONG

The Hodrick-Prescott (HP) filter is a commonly used tool in macroeconomics, and is used to extract a trend component from a time series. In this paper, we derive a new representation of the transformation of the data that is implied by the HP fi lter. This representation highlights that the HP filter is a weighted average plus a number of adjustments that are important near the begin and end of the sample. Using this representation, we characterize the large T behavior of the HP filter and fi nd conditions under which it is asymptotically equivalent to a symmetric weighted average. We fi nd that the cyclical component of the HP fi lter possesses weak dependence properties when the HP filter is applied to a stationary mixing process, a linear deterministic trend process and/or a process with a unit root. This justifi es the use of the HP filter as a tool to achieve weak dependence in a time series and illustrates that the finding in empirical macro that data series tend to have deterministic trends and/or unit roots and the practice of using inference procedures based on the cyclical component of the HP filter are not contradictory. In addition, a large bandwidth approximation to the HP filter is derived, and using this approximation we find an alternative justifi cation for the procedure given in Ravn and Uhlig (2001) for adjusting the bandwidth for the data frequency.