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

Abstract

a b s t r a c tA 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 normalization the least squares estimator for these coefficients has a normal limit distribution. If none of the parameters equals zero then the typical rate of convergence is n.

A Survey of Spatial Unit Roots

“…They also prove that the OLS estimator is asymptotically normally distributed with the convergence rate n when the model is stable, and n 3/2 otherwise. (The simpler model Y k,l = αY k−1,l + βY k,l−1 + ϵ k,l , with possibly α = β was investigated in Baran et al [60], Baran et al [44], Baran and Pap [61] under stable and unstable cases. Under different settings, the limiting distribution of the OLS estimator is normal but has different rates of convergence.…”

Welcome to Aachen

“…We propose a test for m = 2 against m > 2 states for HMMs with state-dependent distributions from a general one-parameter family. Our test for this important problem is an extension to HMMs of the modified likelihood ratio test (LRT) for two states in a finite mixture, as proposed by Chen et al (2004). Its asymptotic distribution theory under the null hypothesis of two states is being derived.…”