### 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 language | English |
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Pages (from-to) | 269-277 |

Number of pages | 9 |

Journal | Statistics |

Volume | 41 |

Issue number | 4 |

DOIs | |

Publication status | Published - 2007 Aug 1 |

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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

- Statistics and Probability
- Statistics, Probability and Uncertainty

### Cite this

*Statistics*,

*41*(4), 269-277. https://doi.org/10.1080/02331880701270515