Asymptotics for Stationary Very Nearly Unit Root Processes

This paper 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 ρn is very near to one in the sense that 1 – ρn = (n–1).

Keywords: Asymptotics, Least squares, Nearly nonstationary, Stationary initial condition, Unit root

JEL Classification Number: C22