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Estimation of spatial ARMA models. (English) Zbl 0776.62074
Let $$Z$$ be the set of all integers. The nonsymmetric half-plane (NSHP) ordering on $$Z^ 2$$ is given by the following rule: One says that $$x=(x_ 1,x_ 2)\leq y=(y_ 1,y_ 2)$$ if $$y-x\in S$$ where $$S=\{t=(t_ 1,t_ s): 1\leq t_ 2$$, or $$t_ 2=0$$ and $$t_ 1>0\}$$. The authors deal with NSHP spatial ARMA models. A method for estimating the orders and parameters of the model is proposed and strong consistency of the estimators is established. The method is based on an inverse model and so the estimation of the innovations is avoided which considerably reduces the computational complexity.
Reviewer: J.Anděl (Praha)

##### MSC:
 62M30 Inference from spatial processes 62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
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