On the Cyclical Properties of Hamilton’s Regression Filter

Abstract

Hamilton (2018) proposes a regression filter (Hamilton filter) as an alternative to the Hodrick-Prescott filter (HP filter). He argues that the Hamilton filter meets all of the objectives desired by users of the HP filter, while addressing its drawbacks. I show that there is a trade-of between these two goals, which has been overlooked. The Hamilton filter does indeed avoid spurious cycles, ad hoc filter settings and end-of-sample bias. However, this comes at a cost. The Hamilton filter may modify fluctuations by altering variances and inducing phase shifts. Furthermore, the exact form of modification can vary across time series.

Keywords: Business cycles, detrending, band pass filter, forecast errors, spurious cycles, phase shifts

JEL Classification: C10, E32, E58, G01