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Gaussian maximum likelihood estimation for ARMA models I: time series

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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

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en

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application/pdf

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http://eprints.lse.ac.uk/5825/1/Gaussian_maximum_likelihood_estimation_for_ARMA_models_I%28LSERO%29.pdf

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