Improved estimation for the autocovariances of a Gaussian stationary process

Masanobu Taniguchi*, Hiroshi Shiraishi, Hiroaki Ogata

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

1 Citation (Scopus)


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
Issue number4
Publication statusPublished - 2007 Aug 1


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

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty


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