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Asymptotics of the sample mean and sample covariance of long-range-dependent series

Part of: Distribution theory

Published online by Cambridge University Press:  14 July 2016

Wen Dai
Wen Dai*
Affiliation:
School of Mathematics and Statistics, University of Sydney, NSW 2006, Australia. Email address: [email protected]
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Abstract

An asymptotic distribution is given for the partial sums of a stationary time-series with long-range dependence. The law of large numbers for the sample covariance of the series is also derived. The results differ from those given elsewhere in relaxing the assumption of the independence of the innovations of the series.

Keywords

Central limit theoremlaws of large numberslong-range dependencesample meansample covariance

MSC classification

Primary: 62E20: Asymptotic distribution theory
Type
Part 7. Time series analysis
Information
Journal of Applied Probability , Volume 41 , Issue A: Stochastic Methods and their Applications , 2004 , pp. 383 - 392
Copyright
Copyright © Applied Probability Trust 2004 

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