Ridge Regression Representations of the Generalized Hodrick-Prescott Filter

Abstract

The Hodrick-Prescott (HP) filter is a popular econometric tool for estimating the trend component of a given time series. Paige and Trindade (2010) present a ridge regression representation of the HP filter, which enhances our understanding of the filter. Schlicht (2005) presents another ridge regression representation of the HP filter. In this paper, we aim to generalize their results. In addition, we present an orthogonal decomposition of the generalized HP trend and newly introduce the pure generalized HP filter.