Kolmogorov-Wiener Filters for Finite Time Series
31 Pages Posted: 5 Aug 2005
Date Written: July 2004
This paper describes a framework of how to optimally implement linear filters for finite time series. The filters under consideration have the property that they minimize the mean squared error compared to some ideal hypothetical filter. It is shown in examples that three commonly used filters, the bandpass filter, the Hodrick-Prescott filter and the digital Butterworth filter need to be adjusted when applied to finite samples of serially correlated or integrated data. An empricial example indicates that the proposed optimal filters improve the end-of-sample performance of standard filters when applied to U.S. GDP data.
Keywords: business cycles, mechanical filters, spectral analysis
JEL Classification: C22
Suggested Citation: Suggested Citation
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Short Term Analysis of Raw Data and Business Cycle Estimation - Part 2: Empirical Implementation (Analyse Conjoncturelle de Données Brutes et Estimation de Cycles Partie 2: Mise en Oeuvre Empirique) (French)