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 the objectives desired by users of the HP filter while avoiding the HP filter's drawbacks. I document a trade-off between (i) avoiding the drawbacks and (ii) meeting all the objectives, which has been overlooked. The Hamilton filter does indeed avoid spurious cycles, ad hoc filter settings, and end-of-sample bias. However, because of this, the Hamilton filter modifies the different frequencies captured in an estimated cyclical component. The filter induces phase shifts and likely alters variances. In parallel, the way the filter modifies typically varies across time series. Within a simulation exercise, I find evidence that these drawbacks of the Hamilton filter can be empirically relevant.

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

JEL Classification: C10, E32, E58, G01