Asymptotic covariance structure of serial correlations in multivariate time series

Abstract

A simple proof of the asymptotic joint normality of any finite set of serial correlations of a general multivariate second-order stationary time series is presented and an explicit formula for the asymptotic covariance between two serial correlations is derived. The latter extends Bartlett's formula for the asymptotic covariance between two sample cross-correlations.