Testing stability in a spatial unilateral autoregressive model

Abstract

Least squares estimator of the stability parameter $\varrho :=|\alpha |+|\beta |$ for a spatial unilateral autoregressive process $X_{k,\ell }=\alpha X_{k-1,\ell }+\beta X_{k,\ell -1}+{\epsilon }_{k,\ell }$ is investigated. Asymptotic normality with a scaling factor $n^{5/4}$ is shown in the unstable case, i.e., when $\varrho =1$, in contrast to the AR(p) model $X_k={\alpha }_1{X}_{k-1}+...+{\alpha }_p{X}_{k-p}+{\epsilon }_k$, where the least squares estimator of the stability parameter $\varrho :={\alpha }_1+...+{\alpha }_p$ is not asymptotically normal in the unstable, i.e., in the unit root case.

References in corpus (1)

• Parameter estimation in a spatial unit root autoregressive model