COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1607

Asymptotics for Stationary Very Nearly Unit Root Processes

Donald W.K. Andrews and Patrik Guggenberger

March 2007

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 rho_n is very near to one in the sense that 1 – rho_n = (n^–1).

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

JEL Classification Number: C22