Improved estimation for the autocovariances of a Gaussian stationary process |
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Authors: | Masanobu Taniguchi Hiroshi Shiraishi Hiroaki Ogata |
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Affiliation: | 1. Department of Mathematical Sciences , School of Science and Engineering, Waseda University , 3-4-1 Okubo Shinjuku-ku, Tokyo, 169-8555, Japan taniguchi@waseda.jp;3. Department of Mathematical Sciences , School of Science and Engineering, Waseda University , 3-4-1 Okubo Shinjuku-ku, Tokyo, 169-8555, Japan |
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Abstract: | For a Gaussian stationary process with mean μ and autocovariance function γ(·), 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 Γ? and Γ?, 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. |
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Keywords: | Gaussian stationary process Autocovariance Spectral density Mean squares error Empirical Bayes estimator James-Stein estimator Shrinkage estimator |
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