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Asymptotic results for spatial ARMA models. (English) Zbl 1093.62083
Summary: Causal quadrantal-type spatial ARMA\((p, q)\) models with independent and identically distributed innovations are considered. In order to select the orders (\(p, q\)) of these models and estimate their autoregressive parameters, estimators of the autoregressive coefficients, derived from the extended Yule-Walker equations are defined. Consistency and asymptotic normality are obtained for these estimators. Then, spatial ARMA model identification is considered and a simulation study is given.

MSC:
62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62M30 Inference from spatial processes
62F12 Asymptotic properties of parametric estimators
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