@article{d51df0eff76e4354bee3b96b79ce756c,
title = "Third order asymptotic properties of maximum likelihood estimators for Gaussian ARMA processes",
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 (⊂ A3) of estimators, we can show that appropriately modified maximum likelihood estimator is always third-order asymptotically efficient in D.",
keywords = "Edgeworth expansion, Gaussian autoregressive moving average processes, Toeplitz matrix, maximum likelihood estimator, residue theorem, spectral density, third order asymptotic efficiency",
author = "Masanobu Taniguchi",
note = "Funding Information: Received March 15, 1984; revised February 20, 1985. AMS 1980 subject classifications. Primary 62Fl2, 62Ml5: secondary 62Ml0, 62EZO. Key words and phrases: Gaussian autoregressive moving average processes, spectral density, Toeplitz matrix, maximum likelihood estimator, third order asymptotic efficiency, Edgeworth expansion, residue theorem *This work was partially supported by Japan Society of Promotion of Science, United States-Japan Cooperative Science Program and Grant-in-Aid of the Ministry of Japan. Copyright: Copyright 2014 Elsevier B.V., All rights reserved.",
year = "1986",
month = feb,
doi = "10.1016/0047-259X(86)90055-2",
language = "English",
volume = "18",
pages = "1--31",
journal = "Journal of Multivariate Analysis",
issn = "0047-259X",
publisher = "Academic Press Inc.",
number = "1",
}