Bartlett correction in the stable second-order autoregressive model with intercept and trend

This paper derives the Bartlett factors that can be used to obtain higher-order improvements for testing hypotheses about the autoregressive (AR) parameters in the stable AR(2) model with possible intercept and linear trend. The factors are obtained for testing hypotheses about individual parameters (phi(1) and phi(2)) as well as their sum. Moreover, the effect of deterministic terms on the correction factors is found explicitly. All corrections are non-decreasing in the AR parameters. Furthermore, the Bartlett corrections for phi(1) and phi(2) tend to infinity as phi(2) approaches 1, whereas the correction for phi(1)+phi(2) tends to infinity as phi(1)+phi(2) is close to 1. The effectiveness of these Bartlett corrections in finite samples is evaluated by simulations.