Locating change-points in Hodrick–Prescott trends with an application to US real GDP: A generalized unobserved components model approach

The trends estimated by the Hodrick–Prescott (HP) filter are smooth by design and it is not easy to pinpoint their change-points. In this study, we locate their change-points by formulating the HP filter as a generalized unobserved components model with error terms of mixtures of normal distributions. We apply the method to US real GDP for the 1947:1–2013:3 period and find that a sequence of mostly negative shocks, rather than a few extraordinary large ones, are responsible for the changes in the US real GDP trend.