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On a spectral density estimate obtained by averaging periodograms

Published online by Cambridge University Press:  14 July 2016

Rainer Dahlhaus
Rainer Dahlhaus*
Affiliation:
Universität Essen
*
∗Postal address: Universität Essen, Fachbereich Mathematik, Postfach 103764, 4300 Essen 1, W. Germany.
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Abstract

A spectral density statistic obtained by averaging periodograms over overlapping time intervals is considered where the periodograms are calculated using a data window. The asymptotic mean square error of this estimate for scale parameter windows is determined and, as an example, it is shown that the use of the Tukey–Hanning window leads partially to a smaller mean square error than a window suggested by Kolmogorov and Zhurbenko. Furthermore the Tukey–Hanning window is independent of the unknown spectral density, which is not the case for the Kolmogorov–Zhurbenko window. The mean square error of this estimate is also less than the mean square error of commonly used window estimates. Finally, a central limit theorem for the estimate is established.

Keywords

STATIONARY PROCESSSPECTRAL ESTIMATEDATA WINDOWMEAN SQUARE ERRORASYMPTOTIC NORMALITY
Type
Research Papers
Information
Journal of Applied Probability , Volume 22 , Issue 3 , September 1985 , pp. 598 - 610
Copyright
Copyright © Applied Probability Trust 1985 

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