Parameter estimation of spatial AR model
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.
stationary martingale difference innovations
scientific article; zbMATH DE number 60807