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ASYMPTOTICS OF SPECTRAL DENSITY ESTIMATES

Published online by Cambridge University Press:  04 November 2009

Weidong Liu and
Wei Biao Wu
Weidong Liu*
Affiliation:
Zhejiang University
Wei Biao Wu
Affiliation:
University of Chicago
*
*Address correspondence to Weidong Liu, Department of Mathematics, Zhejiang University, Huangzhou, Zhejiang, China; e-mail: liuweidong99@gmail.com.
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Abstract

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We consider nonparametric estimation of spectral densities of stationary processes, a fundamental problem in spectral analysis of time series. Under natural and easily verifiable conditions, we obtain consistency and asymptotic normality of spectral density estimates. Asymptotic distribution of maximum deviations of the spectral density estimates is also derived. The latter result sheds new light on the classical problem of tests of white noises.

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Type
ARTICLES
Information
Econometric Theory , Volume 26 , Issue 4 , August 2010, pp. 1218 - 1245
Copyright
Copyright © Cambridge University Press 2009

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