Several least-squares problems related to the Hodrick-Prescott filtering

摘要

The Hodrick-Prescott (HP) filtering is frequently used in macroecono-metrics to decompose time series, such as real gross domestic product, into their trend and cyclical components. Because the HP filtering is a basic econometric tool, it is necessary to have a precise understanding of the nature of it. This article contributes to the literature by listing several (penalized) least-squares problems that are related to the HP filtering, three of which are newly introduced in the article, and showing their properties. We also remark on their generalization.