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

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. This distribution function of the innovation sequence of the linear process satisfies a multivariate regular variation condition. Unlike the univariate case, the limit distibution 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.