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 = ρ n in [0,1) provided (1 - ρ 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 ( n 1 ), 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