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

Schleicher, Christoph, Kolmogorov-Wiener Filters for Finite Time Series (July 2004). Available at SSRN: https://ssrn.com/abstract=769584 or http://dx.doi.org/10.2139/ssrn.769584

Christoph Schleicher (Contact Author)

Bank of England ( email )

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London EC2R 8AH
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