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Asymptotics For Stationary Very Nearly Unit Root Processes, Donald W.K. Andrews, Patrik Guggenberger

Cowles Foundation Discussion Papers

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 ).