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Journal Article

A Central Limit Theorem for Stationary Processes and the Parameter Estimation of Linear Processes

Yuzo Hosoya and Masanobu Taniguchi
The Annals of Statistics
Vol. 10, No. 1 (Mar., 1982), pp. 132-153
Stable URL: http://www.jstor.org/stable/2240505
Page Count: 22
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A Central Limit Theorem for Stationary Processes and the Parameter Estimation of Linear Processes
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Abstract

A central limit theorem is proved for the sample covariances of a linear process. The sufficient conditions for the theorem are described by more natural ones than usual. We apply this theorem to the parameter estimation of a fitted spectral model, which does not necessarily include the true spectral density of the linear process. We also deal with estimation problems for an autoregressive signal plus white noise. A general result is given for efficiency of Newton-Raphson iterations of the likelihood equation.

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