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 (φ1 and φ2) 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 φ1 and φ2 tend to infinity as φ2 approaches 1, whereas the correction for φ1 + φ2 tends to infinity as φ1 + φ2 is close to 1. The effectiveness of these Bartlett corrections in finite samples is evaluated by simulations.