Parameter estimation of spatial AR model
type: Item
instance of: scholarly article
title: Parameter estimation of spatial AR model
zbMATH Open document ID: 0764.62075
author: Jiming Jiang
published in: Chinese Annals of Mathematics. Series B
publication date: 1992-09-27T00:00:00Z
review text: The paper studies consistency and asymptotic normality of the Yule-Walker estimate of the parameters of a spatial AR model defined by \[ X_ t=\sum_{s\in(0,p]} a_ s X_{t-s}+W_ t,\quad t\in N^ 2,\quad p=(p_ 1,p_ 2)\in N^ 2. \] Consistency is established under weak assumptions on the innovations process \((W_ t)\), making use of 2- parameter ergodic theorems. Asymptotic normality is established for the case of stationary martingale difference innovations. The assumptions are weaker than those of \textit{D. Tjostheim} [Adv. Appl. Probab. 10, 130-154 (1978; Zbl 0383.62060) and ibid. 15, 562-584 (1983; Zbl 0525.62084)], who studied strong martingale difference sequence innovations. The present author also claims that those proofs contain gaps.
Mathematics Subject Classification ID: 62M30
Mathematics Subject Classification ID: 62M10
zbMATH DE Number: 60807
zbMATH Keywords: consistency
zbMATH Keywords: asymptotic normality
zbMATH Keywords: Yule-Walker estimate
zbMATH Keywords: spatial AR model
zbMATH Keywords: innovations process
zbMATH Keywords: 2-parameter ergodic theorems
zbMATH Keywords: stationary martingale difference innovations
reviewed by: Herold Dehling
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 60807