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Gaussian maximum likelihood estimation for ARMA models II: spatial processes

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  • Yao, Qiwei
  • Brockwell, Peter J

Abstract

This paper examines the Gaussian maximum likelihood estimator (GMLE) in the context of a general form of spatial autoregressive and moving average (ARMA) processes with finite second moment. The ARMA processes are supposed to be causal and invertible under the half-plane unilateral order, but not necessarily Gaussian. We show that the GMLE is consistent. Subject to a modification to confine the edge effect, it is also asymptotically distribution-free in the sense that the limit distribution is normal, unbiased and has variance depending only on the autocorrelation function. This is an analogue of Hannan's classic result for time series in the context of spatial processes.

Suggested Citation

  • Yao, Qiwei & Brockwell, Peter J, 2006. "Gaussian maximum likelihood estimation for ARMA models II: spatial processes," LSE Research Online Documents on Economics 5416, London School of Economics and Political Science, LSE Library.
    • Handle: RePEc:ehl:lserod:5416
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    File URL: http://eprints.lse.ac.uk/5416/
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    More about this item

    Keywords

    ARMA spatial process; asymptotic normality; consistency; edge effect; Gaussian maximum; likelihood estimator; artingale difference;
    All these keywords.

    JEL classification:

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

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