Time series: theory and methods
Time series: theory and methods
Asymptotic properties of serial covariances for nonlinear stationary processes
Journal of Multivariate Analysis
Deflation-based separation of uncorrelated stationary time series
Journal of Multivariate Analysis
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This paper quantifies the form of the asymptotic covariance matrix of the sample autocovariances in a multivariate stationary time series-the classic Bartlett formula. Such quantification is useful in many statistical inferences involving autocovariances. While joint asymptotic normality of the sample autocovariances is well-known in univariate settings, explicit forms of the asymptotic covariances have not been investigated in the general multivariate non-Gaussian case. We fill this gap by providing such an analysis, bookkeeping all skewness terms. Additionally, following a recent univariate paper by Francq and Zakoian, we consider linear processes driven by non-independent errors, a feature that permits consideration of multivariate GARCH processes.