On the least squares estimator in a nearly unstable sequence of stationary spatial AR models

TL;DR

This paper studies the behavior of the least squares estimator in nearly unstable stationary spatial AR models, showing it converges to a normal distribution under proper normalization, with a typical convergence rate of n.

Contribution

It provides the asymptotic distribution and convergence rate of the least squares estimator in nearly unstable spatial AR models, extending understanding of their statistical properties.

Findings

Estimator converges to a normal distribution after normalization.

Convergence rate is typically n when none of the parameters are zero.

Results apply to sequences where the sum of absolute AR coefficients approaches one.

Abstract

A nearly unstable sequence of stationary spatial autoregressive processes is investigated, when the sum of the absolute values of the autoregressive coefficients tends to one. It is shown that after an appropriate norming the least squares estimator for these coefficients has a normal limit distribution. If none of the parameters equals zero than the typical rate of convergence is n.