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 ρ n is very near to one in the sense that 1 – ρ n = ( n –1 ).
Andrews, Donald W.K. and Guggenberger, Patrik, "Asymptotics for Stationary Very Nearly Unit Root Processes" (2007). Cowles Foundation Discussion Papers. 1901.