Gaussian maximum likelihood estimation for ARMA models. I. Time series

Qiwei Yao and Peter J Brockwell

LSE Research Online Documents on Economics from London School of Economics and Political Science, LSE Library

Abstract: We provide a direct proof for consistency and asymptotic normality of Gaussian maximum likelihood estimators for causal and invertible autoregressive moving-average (ARMA) time series models, which were initially established by Hannan [Journal of Applied Probability (1973) vol. 10, pp. 130–145] via the asymptotic properties of a Whittle's estimator. This also paves the way to establish similar results for spatial processes presented in the follow-up article by Yao and Brockwell published in Bernoulli.

Keywords: ARMA time series models; asymptotic normality; consistency; Gaussian maximum likelihood estimator; innovation algorithm; martingale difference; prewhitening (search for similar items in EconPapers)
JEL-codes: C1 (search for similar items in EconPapers)
Pages: 19 pages
Date: 2006-11
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Citations: View citations in EconPapers (34)

Published in Journal of Time Series Analysis, November, 2006, 27(6), pp. 857 - 875. ISSN: 0143-9782

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