ON THE VARIANCES OF A SPATIAL UNIT ROOT MODEL

Asymptotic properties of the variances of the spatial autoregressive model X(k,l) = alpha X(k-1,l) + beta X(k,l-1) + gamma X(k-1,l-1) + epsilon(k,l) are investigated in the unit root case, that is, where the parameters are on the boundary of the domain of stability that forms a tetrahedron in [- 1, 1](3). The limit of the variance of n(-rho)X([ns],[nt]) is determined, where rho - 1/4 on the interior of the faces of the domain of stability, rho = 1/2 on the edges, and rho = 1 on the vertices.