Estimating the Smoothing Parameter in the So-Called Hodrick-Prescott Filter

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.