On unit roots for spatial autoregressive models (Q860343)

We consider the unit root problem for one rather simple autoregressive model, \[ Y_{t,s}=aY_{t-1,s}+bY_{t,s-1}+\varepsilon_{t,s}, \] on a two-dimensional lattice. We show that the growth of variance of \(Y_{t,s}\) is essentially different from the 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 an autoregressive field on a d-dimensional lattice is different for \(d=2,3\) and \(d\geq 4\).