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Note on the Asymptotic Efficiency of Sample Covariances in Gaussian Vector Stationary Processes

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  • Yoshihide Kakizawa

Abstract

In this note certain results obtained by Porat (J. Time Ser. Anal. 8 (1987), 205–20) and Kakizawa and Taniguchi (J. Time Ser. Anal. 15 (1994), 303–11) concerning the asymptotic efficiency of sample autocovariances of a zero‐mean Gaussian stationary process are extended to the case of m‐vector processes. It is shown that, for Gaussian vector AR(p) processes, the sample autocovariance matrix at lag k is asymptotically efficient if 0 ≤k≤p. Further, none of the sample autocovariance matrices is asymptotically efficient for Gaussian vector MA(q) processes.

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  • 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.
    • Handle: RePEc:bla:jtsera:v:20:y:1999:i:5:p:551-558
    DOI: 10.1111/1467-9892.00156
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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.
    2. Hiroshi Shiraishi & Masanobu Taniguchi, 2008. "Statistical estimation of optimal portfolios for non-Gaussian dependent returns of assets," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 27(3), pages 193-215.
    3. Okui Ryo, 2014. "Asymptotically Unbiased Estimation of Autocovariances and Autocorrelations with Panel Data in the Presence of Individual and Time Effects," Journal of Time Series Econometrics, De Gruyter, vol. 6(2), pages 1-53, July.

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