Third order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes

Masanobu Taniguchi

Journal of Multivariate Analysis, 1986, vol. 18, issue 1, 1-31

Abstract: In this paper we investigate various third-order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes by the third-order Edgeworth expansions of the sampling distributions. We define a third-order asymptotic efficiency by the highest probability concentration around the true value with respect to the third-order Edgeworth expansion. Then we show that the maximum likelihood estimator is not always third-order asymptotically efficient in the class A3 of third-order asymptotically median unbiased estimators. But, if we confine our discussions to an appropriate class D ([subset of] A3) of estimators, we can show that appropriately modified maximum likelihood estimator is always third-order asymptotically efficient in D.

Keywords: Gaussian; autoregressive; moving; average; processes; spectral; density; Toeplitz; matrix; maximum; likelihood; estimator; third; order; asymptotic; efficiency; Edgeworth; expansion; residue; theorem (search for similar items in EconPapers)
Date: 1986
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Citations: View citations in EconPapers (3)

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