How Should we Filter Economic Time Series?

Abstract

Hamilton (2017) criticises the HP filter because of three drawbacks (i. spurious cycles, ii. end-of-sample bias, iii. ad hoc assumptions regarding the smoothing parameter) which, moreover, apply to other popular time series filters as well. As an alternative filter, he proposes a regression filter. I demonstrate that Hamilton's regression filter is partially subject to the same drawbacks (i. and iii.). Furthermore, I illustrate that Hamilton's regression filter does not fulfil established criteria for the desired properties of filters. For instance, in contrast to the HP filter, Hamilton's filter does not approximate the ideal band pass filter, does not have constant cyclical properties across time series, and induces phase shifts. I discuss two refinements to bridge Hamilton's and the established view. For extracting business or financial cycles, I find that a one-sided HP filter and a 1-quarter regression filter can best reconcile both perspectives.

Keywords: detrending, spurious cycles, business cycles, financial cycles, Basel III

JEL Classification: C10, E32, E58, G01