Whittaker Graduation and the Hodrick-Prescott Filter

Hodrick and Prescott (1997) proposed a smoothing method for economic time series that is very similar to graduation, it is usually known as the H-P method. They acknowledged that this method is equivalent to graduation methods and that it had been in use among actuaries. The literature on smoothing methods based on their approach grew separately from the graduation literature, due to the usefulness of identifying economic cycles. Both the Whittaker-Henderson and the H-P methods require the specification of a particular constant, the smoothing constant, usually identified as  . The specification is arbitrary. In this paper we present a Bayesian approach to both methods that is similar to previous analyses but using MCMC methods. In addition Hodrick and Prescott’s  is obtained as a Bayesian estimator. Other concepts from the econometrics literature are introduced for graduation purposes.