Parameter estimation in a spatial unit root autoregressive model

Details Parameter estimation in a spatial unit root autoregressive model Parameter estimation in a spatial unit root autoregressive model

2011-02-16

arxiv.org/abs/1102.3318v3

Mathematics

Statistics Theory

47 pages, 1 figure

Scientific paper

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 $n^{3/2}$.

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