ESTIMATING THE SMOOTHING PARAMETER IN THE SO-CALLED HODRICK-PRESCOTT FILTER

ABSTRACT. This note gives a fairly complete statistical description of the Hodrick-Prescott Filter (1997), originally proposed by Leser (1961). It builds on an approach to seasonal adjustment suggested by Leser (1963) and Schlicht (1981, 1984). A moments estimator for the smoothing pa-rameter is proposed that is asymptotically equivalent to the maximum-likelihood estimator, has a straightforward intuitive interpretation and is more appropriate for short series than the maximum-likelihood estima-tor. The method is illustrated by an application and several simulations. Acknowledgement. I thank Johannes Ludsteck for several helpful sugges-tions and for providing the Mathematica Package (Ludsteck, 2004) used for the computations in this paper. Key words and phrases. Hodrick-Prescott filter, Kalman filtering, Kalman-Bucy, Whittaker-Henderson graduation, spline, state-space models, random walk, time-varying coefficients, adaptive estimation, time-series, seasonal adjustment, trend