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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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##### References:
 [1] Brockwell P. J., Time Series: Theory and Methods., 2. ed. (1987) · Zbl 0604.62083 [2] DOI: 10.1111/j.1467-9892.1991.tb00077.x · Zbl 0729.62081 · doi:10.1111/j.1467-9892.1991.tb00077.x [3] Choi B., ARMA Model Identification (1992) · Zbl 0754.62071 [4] DOI: 10.1080/03610920008832574 · Zbl 0991.62076 · doi:10.1080/03610920008832574 [5] DOI: 10.1016/0167-7152(94)90052-3 · Zbl 0806.62077 · doi:10.1016/0167-7152(94)90052-3 [6] Guyon X., Random Fields on a Network (1995) · Zbl 0839.60003 [7] DOI: 10.1093/biomet/80.1.242 · Zbl 0769.62065 · doi:10.1093/biomet/80.1.242 [8] Huang D. W., Sci. China Ser. A 35 pp 413– (1992) [9] DOI: 10.1111/j.1467-842X.1992.tb01066.x · Zbl 0776.62074 · doi:10.1111/j.1467-842X.1992.tb01066.x [10] DOI: 10.1080/03610929508831600 · Zbl 0937.62641 · doi:10.1080/03610929508831600 [11] DOI: 10.2307/1426722 · Zbl 0383.62060 · doi:10.2307/1426722 [12] DOI: 10.2307/1426619 · Zbl 0525.62084 · doi:10.2307/1426619 [13] DOI: 10.2307/2287515 · Zbl 0471.62088 · doi:10.2307/2287515
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