Bartlett correction in the stable AR(1) model with intercept and trend

The Bartlett correction is derived for testing hypotheses about the autoregressive parameter ρ in the stable: (i) AR(1) model; (ii) AR(1) model with intercept; (iii) AR(1) model with intercept and linear trend. The correction is found explicitly as a function of ρ. In the models with deterministic terms, the correction factor is asymmetric in ρ. Furthermore, the Bartlett correction is monotonic increasing in ρ and tends to infinity when ρ approaches the stability boundary of 1. Simulation results indicate that the Bartlett corrections are useful in controlling the size of the LR statistic in small samples.