Approximate confidence sets for a stationary AR process

Abstract

Approximate confidence intervals are derived for the autoregressive parameters of a stationary, Gaussian auto-regressive process of arbitrary order and shown to be asymptotically correct to order o(1/n), where n is the sample size. Simulation studies are included for small and moderate sample sizes for the case of two auto-regressive parameters, and these indicate excellent approximation for sample sizes as small as n = 10,20. The convergence is in the very weak sense, and the derivation differs from most existing work through its direct focus on Studentized estimation error and its use of Stein’s identity.