Uniform Limit Theory for Stationary Autoregression

Abstract. First order autoregression is shown to satisfy a limit theory which is uniform over stationary values of the autoregressive coefficient ρ = ρ_n ∈ 0, 1) provided (1 ? ρ_n)n → ∞. This extends existing Gaussian limit theory by allowing for values of stationary ρ that include neighbourhoods of unity provided they are wider than O(n^?1), even by a slowly varying factor. Rates of convergence depend on ρ and are at least but less than n. Only second moments are assumed, as in the case of stationary autoregression with fixed ρ.