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This paper proposes a novel derivation of the Hodrick-Prescott (HP) minimization problem which leads to a generalization of the Hodrick-Prescott filter. The main result is the development of a new filter to extract a localized maximum-likelihood estimate of the cycle from a series. This new filter, the multivariate normal cyclical (MNC) filter, makes only a general assumption about the cyclical nature of the series. The output from this filtering procedure is from a nonlinear optimization routine.

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