On the variances of a spatial unit root model

Abstract

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 $\varrho =1$.

Cited by in corpus (2)

• Parameter estimation in a spatial unit root autoregressive model
• First-order planar autoregressive model