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Etude asymptotique de certains estimateurs dans des modèles ARMA spatiaux

Abstract : We study the asymptotic behaviour of some statistics for spatial quadrantal ARMA models with independent and identically distributed innovations or more generally strong martingale innovations. After giving a review of limit theorems for lattice martingales, we establish a central limit theorem and an invariance principle under the conditional Lindeberg condition for strong lattice martingales. For a better understanding of our study on quadrantal ARMA random fields, we recall various results on estimation and identification for others spatial ARMA models. Then, in order to select orders and estimate autoregressive coefficients in spatial quadrantal ARMA models, we introduce a new estimator based on a derivation of extended Yule-Walker equations and prove that it is consistent and asymptotically normal. Finally, we illustrate with graphic representations the behaviour of several spatial ARMA models and present a study of procedures for their identification.
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https://tel.archives-ouvertes.fr/tel-00007866
Contributor : Aude Illig <>
Submitted on : Wednesday, December 29, 2004 - 11:23:04 AM
Last modification on : Friday, January 10, 2020 - 9:08:06 PM
Long-term archiving on: : Friday, April 2, 2010 - 8:52:41 PM

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  • HAL Id : tel-00007866, version 1

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Aude Illig. Etude asymptotique de certains estimateurs dans des modèles ARMA spatiaux. Mathématiques [math]. INSA de Toulouse, 2004. Français. ⟨tel-00007866⟩

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