This is the program for the 2010 Joint Statistical Meetings in Vancouver, British Columbia.

Abstract Details

Activity Number: 240
Type: Contributed
Date/Time: Monday, August 2, 2010 : 2:00 PM to 3:50 PM
Sponsor: Business and Economic Statistics Section
Abstract - #306485
Title: The Hodrick-Prescott Filter: A Special Case of Penalized Spline Smoothing
Author(s): A. Alexandre Trindade*+ and Robert Paige
Companies: Texas Tech University and Missouri University of Science and Technology
Address: Department of Mathematics & Statistics, Lubbock, TX, 79409-1042,
Keywords: semiparametric model ; estimating equation ; saddlepoint approximation
Abstract:

We prove that the Hodrick-Prescott Filter (HPF), a commonly used method for smoothing econometric time series, is a special case of a linear penalized spline model. The well-known linear mixed model formulation then furnishes a rich variety of ready-made estimation methods for the smoothing parameter, particularly REML and GCV. This has profound implications for users of HPF, who have hitherto typically relied on subjective choice. We also demonstrate a new method for construction of confidence intervals, akin to a parametric bootstrap where Monte Carlo simulation is replaced by saddlepoint approximation, and provides a fast and accurate alternative to exact methods when they exist, e.g. REML. It is also the only computationally feasible method when no other methods, exact or otherwise, exist, e.g. GCV. We demonstrate with the GNP series originally analyzed by Hodrick & Prescott (1997).


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