On the variances of a spatial unit root model

Details On the variances of a spatial unit root model On the variances of a spatial unit root model

2010-06-29

arxiv.org/abs/1006.5730v3

Mathematics

Statistics Theory

Scientific paper

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 $\varrho =1$.

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