Multivariate versions of Bartlett’s formula
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.
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Volume (Year): 105 (2012)
Issue (Month): 1 ()
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References listed on IDEAS
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- Giraitis, Liudas & Kokoszka, Piotr & Leipus, Remigijus, 2000. "Stationary Arch Models: Dependence Structure And Central Limit Theorem," Econometric Theory, Cambridge University Press, vol. 16(01), pages 3-22, February.
- Francq, Christian & Zakoian, Jean-Michel, 2009.
"Bartlett's formula for a general class of non linear processes,"
13224, University Library of Munich, Germany.
- Christian Francq & Jean-Michel Zakoïan, 2009. "Bartlett's formula for a general class of nonlinear processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 30(4), pages 449-465, 07.
- Chanda, K. C., 1993. "Asymptotic Properties of Serial Covariances for Nonlinear Stationary Processes," Journal of Multivariate Analysis, Elsevier, vol. 47(1), pages 163-171, October.
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