  Spatial unilateral autoregressive model $X_{k,\ell}=\alpha X_{k-1,\ell}+\beta
X_{k,\ell-1}+\gamma X_{k-1,\ell-1}+\epsilon_{k,\ell}$ is investigated in the
unit root case, that is when the parameters are on the boundary of the domain
of stability that forms a tetrahedron with vertices $(1,1,-1), \ (1,-1,1),\
(-1,1,1)$ and $(-1,-1,-1)$. It is shown that the limiting distribution of the
least squares estimator of the parameters is normal and the rate of convergence
is $n$ when the parameters are in the faces or on the edges of the tetrahedron,
while on the vertices the rate is $n^{3/2}$.
