Cyclical Dynamics and Trend/Cycle Definitions: Comparing the HP and Hamilton Filters

Abstract

When used for business cycle estimation, the Hodrick–Prescott (HP) filter is frequently accused of introducing spurious dynamics in the cyclical component. Hamilton (Rev Econ Stat 100(5):831–843, 2018) suggests a regression-based filter that is stated to lack all the drawbacks of the HP filter. The current paper documents that similar dynamics can be found in the cyclical component of HP-filtered and Hamilton-filtered series when the filters are applied to identical time series for which it can be argued that there should exist no such dynamics. The results indicate that, if the sheer magnitude of the cyclical dynamics from the HP filter is deemed problematic then the cyclical dynamics of Hamilton-filtered series could be equally problematic. While using a different definition of trend and cycle components can explain the dynamics of the Hamilton cycle, this definition is not always innocuous, and choosing between the two filters may, as a consequence, turn out to be harder than it first may seem.