The Missing Cycle in the HP Filter and the Measurement of Cyclically-Adjusted Budget Balances

Abstract

The HP filter suffers from a pro-cyclical bias in end-of-sample trend estimates. This paper argues that this feature is related to the 'missing cycle' in the stochastic model of the filter. The paper suggest an extensions of the HP filter by including a stochastic cycle component in the underlying model of the filter. As a consequence, the derived trend and cyclical components are more consistent with the underlying filter model, and the end¬point¬behavior improves significantly because the pro¬cyclical bias in end-of-sample trend estimates is virtually removed.