GAUSSIAN INFERENCE IN AR(1) TIME SERIES WITH OR WITHOUT A UNIT ROOT

This paper introduces a simple first-difference-based approach to estimation and inference for the AR(1) model. The estimates have virtually no finite-sample bias and 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 <inline-graphic>null</inline-graphic> rate of convergence. En route, a useful central limit theorem (CLT) for sample covariances of linear processes is given, following Phillips and Solo (1992, <italic>Annals of Statistics</italic>, 20, 971–1001). The approach also has useful extensions to dynamic panels.