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

Title : ASYMPTOTIC INFERENCE FOR NEARLY UNSTABLE AR ( p ) PROCESSES

In this paper nearly unstable AR(p) processes (in other words, models with characteristic roots near the unit circle) are studied. Our main aim is to describe the asymptotic behaviour of the least squares estimators of the coefficients. A convergence result is presented for the general complex-valued case. The limit distribution is given by the help of some continuous time AR processes. We appl...

Asymptotic Inference for a Nearly Unstable Sequence of Stationary Spatial Ar Models

Asymptotic Inference for Nearly Unstable Inar(1) Models

The first–order integer–valued autoregressive (INAR(1)) process is investigated, where the autoregressive coefficient is close to one. It is shown that the limiting distribution of the conditional least–squares estimator for this coefficient is normal and, in contrast to the familiar AR(1) process, the rate of convergence is n. Finally, the nearly critical Galton–Watson process with unobservabl...

Testing stability in a spatial unilateral autoregressive model

Least squares estimator of the stability parameter ̺ := |α|+ |β| for a spatial unilateral autoregressive process Xk,l = αXk−1,l +βXk,l−1 +εk,l is investigated and asymptotic normality with a scaling factor n5/4 is shown in the unstable case ̺ = 1. The result is in contrast to the unit root case of the AR(p) model Xk = α1Xk−1+ · · ·+αpXk−p+εk, where the limiting distribution of the least squares e...

Asymptotic inference for an unstable triangular spatial AR model

A spatial autoregressive process is investigated, where the autoregressive coefficients are equal, and their sum is one. It is shown that the limiting distribution of the least squares estimator for this coefficient is normal and, in contrast to the doubly geometric process, the rate of convergence is n−5/4.