Validity of Edgeworth expansions of minimum contrast estimators for Gaussian ARMA processes

Masanobu Taniguchi

Journal of Multivariate Analysis, 1987, vol. 21, issue 1, 1-28

Abstract: Let {Xt} be a Gaussian ARMA process with spectral density f[theta]([lambda]), where [theta] is an unknown parameter. To estimate [theta] we propose a minimum contrast estimation method which includes the maximum likelihood method and the quasi-maximum likelihood method as special cases. Let [theta][tau] be the minimum contrast estimator of [theta]. Then we derive the Edgewroth expansion of the distribution of [theta][tau] up to third order, and prove its valldity. By this Edgeworth expansion we can see that this minimum contrast estimator is always second-order asymptotically efficient in the class of second-order asymptotically median unbiased estimators. Also the third-order asymptotic comparisons among minimum contrast estimators will be discussed.

Keywords: Gaussian; ARMA; processes; maximum; likelihood; estimator; minimum; contrast; estimator; Edgeworth; expansion (search for similar items in EconPapers)
Date: 1987
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Citations: View citations in EconPapers (5)

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