Parameter estimation in a spatial unit root autoregressive model
arXiv:1102.3318 · doi:10.1016/j.jmva.2012.01.022
Abstract
Spatial unilateral autoregressive model $X_{k,\ell}=αX_{k-1,\ell}+βX_{k,\ell-1}+γX_{k-1,\ell-1}+ε_{k,\ell}$ 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 $n^{3/2}$.
47 pages, 1 figure