COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 1475

Uniform Limit Theory for Stationary Autoregression

Liudas Giraitis and Peter C. B. Phillips

July 12, 2004

First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient rho = rho_n in [0,1) provided (1 - rho_n)n approaches infinity. This extends existing Gaussian limit theory by allowing for values of stationary rho that include neighbourhoods of unity provided they are wider than (n¹), even by a slowly varying factor. Rates of convergence depend on rho and are at least squareroot of /n but less than n. Only second moments are assumed, as in the case of stationary autoregression with fixed rho.

AMS Subject Classifications: Primary 62M10; Secondary 60F15

JEL Classifications: C22

Keywords and Phrases: Autoregression, Gaussian limit theory, local to unity, uniform limit