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

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  • Yao, Qiwei
  • Brockwell, Peter J

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.

Suggested Citation

  • Yao, Qiwei & Brockwell, Peter J, 2006. "Gaussian maximum likelihood estimation for ARMA models. I. Time series," LSE Research Online Documents on Economics 57580, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:57580
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    File URL: http://eprints.lse.ac.uk/57580/
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    More about this item

    Keywords

    ARMA time series models; asymptotic normality; consistency; Gaussian maximum likelihood estimator; innovation algorithm; martingale difference; prewhitening;
    All these keywords.

    JEL classification:

    • C1 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General

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