The Hodrick-Prescott Filter, a Generalisation, and a New Procedure for Extracting an Empirical Cycle from a Series

This paper proposes a novel derivation of the Hodrick-Prescott, Department of Economics (HP) minimisation problem which leads to a generalisation of the Hodrick-Prescott filter. The main result is the development of a new filter to extract a localised maximum likelihood estimate of the cycle from a series. This new filter, the Multivariate Normal Cyclical (MNC) filter makes only a very general assumption about the cyclical nature of the series. Unlike most other filters, it does not make any explicit assumption about the nature of the trend component of the series.