COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1546

Gaussian Inference in AR(1) Time Series with or without a Unit Root

Peter C. B. Phillips
Cowles Foundation, Yale University; University of York & University of Auckland
Chirok Han
Victoria University of Wellington

January 2006

This note introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite sample bias, are not sensitive to initial conditions, and the approach has the unusual advantage that a Gaussian central limit theory applies and is continuous as the autoregressive coefficient passes through unity with a uniform /n rate of convergence. En route, a useful CLT for sample covariances of linear processes is given, following Phillips and Solo (1992). The approach also has useful extensions to dynamic panels.

Keywords: Autoregression, Differencing, Gaussian limit, Mildly explosive processes, Uniformity, Unit root

JEL Classification Numbers: C22