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 -> 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(-1)), even by a slowly varying factor. Rates of convergence depend on rho and are at least root n but less than n. Only second moments are assumed, as in the case of stationary autoregression with fixed rho.