On unit roots for spatial autoregressive models

In this paper we consider the unit root problem for one rather simple autoregressive model Y t , s = aY t - 1 , s + bY t , s - 1 + ɛ t , s on a two-dimensional lattice. We show that the growth of variance of Y t , s is essentially different from corresponding growth in the unit root case for AR ( 1 ) or AR ( 2 ) time series models. We also show that the dimension of the lattice plays an important role: the growth of variance of autoregressive field on a d-dimensional lattice is different for d = 2 , 3 and d ≥ 4 .