J. Japan Statist. Soc., Vol. 35 (No. 1), pp. 99-119, 2005

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

Ekkehart Schlicht

Abstract. This note gives a statistical description of the Hodrick-Prescott Filter (1997), originally proposed by Leser (1961). A maximum-likelihood estimator is derived and a related moments estimator is proposed that has a straightforward intuitive interpretation and coincides with the maximum-likelihood estimator for long time series. The method is illustrated by an application and several simulations. The statistical treatment in the state-space tradition implies some scepticism regarding the interpretation in terms of low-frequency filtering.

Key words and phrases: Adaptive estimation, Hodrick-Prescott filter,Kalman-Bucy, Kalman filtering, orthogonal parametrization, random walk, seasonal adjustment, spline, state-space models, time-series, time-varying coefficients,trend, Whittaker- Henderson graduation.

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