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Asymptotic Efficiency Of The Sample Covariances In A Gaussian Stationary Process

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  • Yoshihide Kakizawa
  • Masanobu Taniguchi

Abstract

. This paper deals with the asymptotic efficiency of the sample autocovariances of a Gaussian stationary process. The asymptotic variance of the sample autocovariances and the Cramer–Rao bound are expressed as the integrals of the spectral density and its derivative. We say that the sample autocovariances are asymptotically efficient if the asymptotic variance and the Cramer–Rao bound are identical. In terms of the spectral density we give a necessary and sufficient condition that they are asymptotically efficient. This condition is easy to check for various spectra.

Suggested Citation

  • Yoshihide Kakizawa & Masanobu Taniguchi, 1994. "Asymptotic Efficiency Of The Sample Covariances In A Gaussian Stationary Process," Journal of Time Series Analysis, Wiley Blackwell, vol. 15(3), pages 303-311, May.
  • Handle: RePEc:bla:jtsera:v:15:y:1994:i:3:p:303-311
    DOI: 10.1111/j.1467-9892.1994.tb00195.x
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    Cited by:

    1. 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.
    2. 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.
    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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