Limit theory for the sample covariance and correlation matrix functions of a class of multivariate linear processes

1 January 1990

journal article
research article
Published by Taylor & Francis in Communications in Statistics. Stochastic Models

Vol. 6 (3) , 483-497
https://doi.org/10.1080/15326349908807158

Abstract

The limit distribution of the sample covariance and correlation matrix functions of a class of multivariate linear processes having a finite second but infinite fourth moment is derived. The distribution function of the innnovation sequence of the linear process satisfies a multivariate regular variation condition. Unlike the univariate case, the limit distribution for the sample correlation matrix function is nonnormal stable. In addition, a stationary 1-dependent sequence of random variables with finite variance is constructed for which the sample correlation function has a nonnormal stable limit distribution.

Keywords

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