Uniform Limit Theory for Stationary Autoregression

First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient rho = rho_n is an element of [0, 1) provided (1 - rho_n)n goes to infinity. This extends existing Gaussian limit theory by allowing for values of stationary rho that include neighbourhoods of unity provided they are wider than O(n-super- - 1), even by a slowly varying factor. Rates of convergence depend on rho and are at least but less than n. Only second moments are assumed, as in the case of stationary autoregression with fixed rho. Copyright 2006 Blackwell Publishing Ltd.