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Multivariate versions of Bartlett’s formula

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  • Su, Nan
  • Lund, Robert
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    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.

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    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X11001679
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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Multivariate Analysis.

    Volume (Year): 105 (2012)
    Issue (Month): 1 ()
    Pages: 18-31

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    Handle: RePEc:eee:jmvana:v:105:y:2012:i:1:p:18-31

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    Related research

    Keywords: Asymptotic normality; Multivariate stationarity; Sample autocorrelations;

    References

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    1. Francq, Christian & Zakoian, Jean-Michel, 2009. "Bartlett's formula for a general class of non linear processes," MPRA Paper 13224, University Library of Munich, Germany.
    2. 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.
    3. 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.
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    Cited by:
    1. Miettinen, Jari & Nordhausen, Klaus & Oja, Hannu & Taskinen, Sara, 2012. "Statistical properties of a blind source separation estimator for stationary time series," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1865-1873.

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