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 ρ = ρn in [0,1) provided (1 - ρn)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 ρ.