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Covariances Estimation for Long-Memory Processes

Part of: Stochastic processes Limit theorems Inference from stochastic processes

Published online by Cambridge University Press:  01 July 2016

Wei Biao Wu ,
Yinxiao Huang  and
Wei Zheng
Wei Biao Wu*
Affiliation:
University of Chicago
Yinxiao Huang*
Affiliation:
University of Chicago
Wei Zheng*
Affiliation:
University of Illinois at Chicago
*
∗ Postal address: Department of Statistics, University of Chicago, Chicago, IL 60637, USA.
∗ Postal address: Department of Statistics, University of Chicago, Chicago, IL 60637, USA.
∗∗∗ Postal address: Department of Mathematics, Statistics, and Computer Science, University of Illinois at Chicago, 851 S. Morgan Street, Chicago, IL 60607-7045, USA.
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Abstract

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For a time series, a plot of sample covariances is a popular way to assess its dependence properties. In this paper we give a systematic characterization of the asymptotic behavior of sample covariances of long-memory linear processes. Central and noncentral limit theorems are obtained for sample covariances with bounded as well as unbounded lags. It is shown that the limiting distribution depends in a very interesting way on the strength of dependence, the heavy-tailedness of the innovations, and the magnitude of the lags.

Keywords

Asymptotic normalitycovariancedichotomylinear processlong-range dependenceRosenblatt distribution

MSC classification

Primary: 60F05: Central limit and other weak theorems 62M10: Time series, auto-correlation, regression, etc.
Secondary: 60G10: Stationary processes
Type
General Applied Probability
Information
Advances in Applied Probability , Volume 42 , Issue 1 , March 2010 , pp. 137 - 157
Copyright
Copyright © Applied Probability Trust 2010 

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