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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.

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  • 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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    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. Yoshihide Kakizawa, 1999. "Note on the Asymptotic Efficiency of Sample Covariances in Gaussian Vector Stationary Processes," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 551-558, September.
    4. 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.
    5. 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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    1. Alessandra Luati & Francesca Papagni & Tommaso Proietti, 2024. "Efficient nonparametric estimation of generalised autocovariances," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 36(1), pages 23-38, January.

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