Filtering economic time series: On the cyclical properties of Hamilton's regression filter and the Hodrick-Prescott filter

The Hamilton (H) filter is proposed as an alternative to the Hodrick-Prescott (HP) filter. It is designed to meet all of the objectives desired by users of the HP filter while avoiding its drawbacks (spurious dynamics, ad hoc filter settings, end-of-sample bias). I document a trade-off that has been overlooked: Addressing the HP filter's drawbacks means that the H filter cannot fulfill all of the desired objectives. It modifies different frequencies captured in an estimated cyclical component by inducing phase shifts and by likely altering variances. Typically, these modifications vary across time series. Through both simulation and real data exercises, I illustrate each filter's cyclical properties.