Covariances estimation for long-memory processes
Wei Biao Wu, Yinxiao Huang, and Wei Zheng
Source: Adv. in Appl. Probab. Volume 42, Number 1
(2010), 137-157.
Abstract
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.
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Keywords: Asymptotic normality; covariance; dichotomy; linear process; long-range dependence; Rosenblatt distribution
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Permanent link to this document: http://projecteuclid.org/euclid.aap/1269611147
Digital Object Identifier: doi:10.1239/aap/1269611147
Zentralblatt MATH identifier: 05717821
Mathematical Reviews number (MathSciNet): MR2666922
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