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 parameter 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 estimator. The method is illustrated by an application and several simulations.
Hodrick-Prescott filter Kalman filter Kalman-Bucy Whittaker-Henderson graduation spline state-space models random walk time-varying coefficients adaptive estimation time-series seasonal adjustment trend