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On the asymptotic properties of multivariate sample autocovariances

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  • Boshnakov, Georgi N.

Abstract

We show that if a process can be obtained by filtering an autoregressive process, then the asymptotic distribution of sample autocovariances of the former is the same as the asymptotic distribution of linear combinations of sample autocovariances of the latter. This result is used to show that for small lags the sample autocovariances of the filtered process have the same asymptotic distribution as estimators utilizing more information (observations on the associated autoregression process and knowledge of the parameters of the filter). In particular, for a Gaussian ARMA process the first few sample autocovariances are jointly asymptotically efficient.

Suggested Citation

  • Boshnakov, Georgi N., 2005. "On the asymptotic properties of multivariate sample autocovariances," Journal of Multivariate Analysis, Elsevier, vol. 92(1), pages 42-52, January.
    • Handle: RePEc:eee:jmvana:v:92:y:2005:i:1:p:42-52
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    References listed on IDEAS

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    1. A. M. Walker, 1995. "On Results Of Porat Concerning Asymptotic Efficiency Of Sample Covariances Of Gaussian Arma Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 16(2), pages 237-248, March.
    2. Georgi Boshnakov, 1996. "Bartlett's formulae—Closed forms and recurrent equations," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 48(1), pages 49-59, March.
    3. Boshnakov, Georgi N., 1996. "The asymptotic covariance matrix of the multivariate serial correlations," Stochastic Processes and their Applications, Elsevier, vol. 65(2), pages 251-258, December.
    4. Boaz Porat, 1987. "Some Asymptotic Properties Of The Sample Covariances Of Gaussian Autoregressive Moving‐Average Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 8(2), pages 205-220, March.
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    Cited by:

    1. Alessandra Luati & Francesca Papagni & Tommaso Proietti, 2021. "Efficient Nonparametric Estimation of Generalized Autocovariances," CEIS Research Paper 515, Tor Vergata University, CEIS, revised 14 Oct 2021.

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