Asymptotics for stationary very nearly unit root processes

Abstract

This article considers a mean zero stationary first-order autoregressive (AR) model. It is shown that the least squares estimator and t statistic have Cauchy and standard normal asymptotic distributions, respectively, when the AR parameter rho_n is very near to one in the sense that 1 - rho_n = o(n-super- - 1). Copyright 2007 The Author Journal compilation 2007 Blackwell Publishing Ltd.