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On accepting the edge-effect (for the inference of ARMA-type processes in Z2)

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  • Dimitriou-Fakalou, Chrysoula

Abstract

The edge-effect interrupts the theory of (weakly) stationary processes indexed in the (infinite) two-dimensional lattice. The bias of the maximum likelihood estimators (with asymptotics increasing on both sides), does not seemingly tend to zero faster than their standard error. To deal with it, weights are applied on the computable innovations, such that all the contributions of the same bias are squeezed to become equivalent to that of one observation. As a result, the edge-effect appearance in the form of the speed of the estimators’ bias (to a finite bound) following the augmentation of observations on one axis only, becomes the base for the new solution to the problem. What remains to be seen, is how these weights affect other properties, such as the asymptotic distribution and variance of the proposed estimators.

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  • 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.
    • Handle: RePEc:eee:ecosta:v:10:y:2019:i:c:p:53-70
    DOI: 10.1016/j.ecosta.2018.03.001
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    References listed on IDEAS

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    1. 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.
    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 II: spatial processes," LSE Research Online Documents on Economics 5416, London School of Economics and Political Science, LSE Library.
    5. 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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