Improved estimation for the autocovariances of a Gaussian stationary process

Masanobu Taniguchi, Hiroshi Shiraishi, Hiroaki Ogata

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    Abstract

    For a Gaussian stationary process with mean μ and autocovariance function λ(̇), we consider to improve the usual sample autocovariances with respect to the mean squares error (MSE) loss. For the cases μ=0 and μ ≠0, we propose sort of empirical Bayes type estimators γ̂ and γ̃, respectively. Then their MSE improvements upon the usual sample autocovariances are evaluated in terms of the spectral density of the process. Concrete examples for them are provided. We observe that if the process is near to a unit root process the improvement becomes quite large. Thus, consideration for estimators of this type seems important in many fields, e.g., econometrics.

    Original languageEnglish
    Pages (from-to)269-277
    Number of pages9
    JournalStatistics
    Volume41
    Issue number4
    DOIs
    Publication statusPublished - 2007 Aug

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    Keywords

    • Autocovariance
    • Empirical Bayes estimator
    • Gaussian stationary process
    • James-Stein estimator
    • Mean squares error
    • Shrinkage estimator
    • Spectral density

    ASJC Scopus subject areas

    • Mathematics(all)
    • Statistics and Probability

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