The Annals of Statistics

On the Second Order Asymptotic Efficiency of Estimators of Gaussian ARMA Processes

Masanobu Taniguchi

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In this paper we investigate an optimal property of maximum likelihood and quasi-maximum likelihood estimators of Gaussian autoregressive moving average processes by the second order approximation of the sampling distribution. It is shown that appropriate modifications of these estimators for Gaussian ARMA processes are second order asymptotically efficient if efficiency is measured by the degree of concentration of the sampling distribution up to second order. This concept of efficiency was introduced by Akahira and Takeuchi (1981).

Article information

Ann. Statist., Volume 11, Number 1 (1983), 157-169.

First available in Project Euclid: 12 April 2007

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Zentralblatt MATH identifier


Primary: 62F12: Asymptotic properties of estimators
Secondary: 62M15: Spectral analysis 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 62E20: Asymptotic distribution theory

Gaussian autoregressive moving average processes spectral density periodogram Toplitz matrix maximum likelihood estimator quasi-maximum likelihood estimator second order asymptotic efficiency Gram-Charlier expansion residue theorem


Taniguchi, Masanobu. On the Second Order Asymptotic Efficiency of Estimators of Gaussian ARMA Processes. Ann. Statist. 11 (1983), no. 1, 157--169. doi:10.1214/aos/1176346066.

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