Multivariate versions of Bartlett’s formula

Nan Su and Robert Lund

Journal of Multivariate Analysis, 2012, vol. 105, issue 1, 18-31

Abstract: 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.

Keywords: Asymptotic normality; Multivariate stationarity; Sample autocorrelations (search for similar items in EconPapers)
Date: 2012
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Citations: View citations in EconPapers (5)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:jmvana:v:105:y:2012:i:1:p:18-31

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DOI: 10.1016/j.jmva.2011.08.008

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