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Modified Gaussian likelihood estimators for ARMA models on

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  • Dimitriou-Fakalou, Chrysoula

Abstract

For observations from an auto-regressive moving-average process on any number of dimensions, we propose a modification of the Gaussian likelihood, which when maximized corrects the edge-effects and fixes the order of the bias for the estimators derived. We show that the new estimators are not only consistent but also asymptotically normal for any dimensionality. A classical one-dimensional, time series result for the variance matrix is established on any number of dimensions and guarantees the efficiency of the estimators, if the original process is Gaussian. We have followed a model-based approach and we have used finite numbers for the corrections per dimension, which are especially made for the case of the auto-regressive moving-average models of fixed order.

Suggested Citation

  • Dimitriou-Fakalou, Chrysoula, 2009. "Modified Gaussian likelihood estimators for ARMA models on," Stochastic Processes and their Applications, Elsevier, vol. 119(12), pages 4149-4175, December.
    • Handle: RePEc:eee:spapps:v:119:y:2009:i:12:p:4149-4175
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
    4. Yao, Qiwei & Brockwell, Peter J., 2006. "Gaussian maximum likelihood estimation for ARMA models I: time series," LSE Research Online Documents on Economics 5825, London School of Economics and Political Science, LSE Library.
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    Cited by:

    1. Abdelouahab Bibi & Karima Kimouche, 2014. "On stationarity and second-order properties of bilinear random fields," Statistical Inference for Stochastic Processes, Springer, vol. 17(3), pages 221-244, October.
    2. Dimitriou-Fakalou, Chrysoula, 2019. "On accepting the edge-effect (for the inference of ARMA-type processes in Z2)," Econometrics and Statistics, Elsevier, vol. 10(C), pages 53-70.
    3. Jentsch, Carsten & Meyer, Marco, 2021. "On the validity of Akaike’s identity for random fields," Journal of Econometrics, Elsevier, vol. 222(1), pages 676-687.

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