  The asymptotic properties of the variances of the spatial autoregressive
model $X_{k,\ell}=\alpha X_{k-1,\ell}+\beta X_{k,\ell-1}+\gamma
X_{k-1,\ell-1}+\epsilon_{k,\ell}$ are investigated in the unit root case, that
is when the parameters are on the boundary of domain of stability that forms a
tetrahedron in $[-1,1]^3$. The limit of the variance of
$n^{-\varrho}X_{[ns],[nt]}$ is determined, where on the interior of the faces
of the domain of stability $\varrho=1/4$, on the edges $\varrho =1/2$, while on
the vertices $\varrho =1$.
