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Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series

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  • Qiwei Yao
  • Peter J. Brockwell

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 [Bernoulli (2006) in press].

Suggested Citation

  • Qiwei Yao & Peter J. Brockwell, 2006. "Gaussian Maximum Likelihood Estimation For ARMA Models. I. Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 27(6), pages 857-875, November.
    • Handle: RePEc:bla:jtsera:v:27:y:2006:i:6:p:857-875
    DOI: 10.1111/j.1467-9892.2006.00492.x
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