### 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 |

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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

### Cite this

*Statistics*,

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

**Improved estimation for the autocovariances of a Gaussian stationary process.** / Taniguchi, Masanobu; Shiraishi, Hiroshi; Ogata, Hiroaki.

Research output: Contribution to journal › Article

*Statistics*, vol. 41, no. 4, pp. 269-277. https://doi.org/10.1080/02331880701270515

}

TY - JOUR

T1 - Improved estimation for the autocovariances of a Gaussian stationary process

AU - Taniguchi, Masanobu

AU - Shiraishi, Hiroshi

AU - Ogata, Hiroaki

PY - 2007/8

Y1 - 2007/8

N2 - 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.

AB - 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.

KW - Autocovariance

KW - Empirical Bayes estimator

KW - Gaussian stationary process

KW - James-Stein estimator

KW - Mean squares error

KW - Shrinkage estimator

KW - Spectral density

UR - http://www.scopus.com/inward/record.url?scp=34547820939&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=34547820939&partnerID=8YFLogxK

U2 - 10.1080/02331880701270515

DO - 10.1080/02331880701270515

M3 - Article

AN - SCOPUS:34547820939

VL - 41

SP - 269

EP - 277

JO - Statistics

JF - Statistics

SN - 0233-1888

IS - 4

ER -