BARTLETT CORRECTION IN THE STABLE AR(1) MODEL WITH INTERCEPT AND TREND

Bartlett corrections are derived for testing hypotheses about the autoregressive parameter <italic>ρ</italic> in the stable (a) AR(1) model, (b) AR(1) model with intercept, (c) AR(1) model with intercept and linear trend. The correction is found explicitly as a function of <italic>ρ</italic>. In the models with deterministic terms, the correction factor is asymmetric in <italic>ρ</italic>. Furthermore, the Bartlett correction is monotonically increasing in <italic>ρ</italic> and tends to infinity when <italic>ρ</italic> approaches the stability boundary of + 1. Simulation results indicate that the Bartlett corrections are useful in controlling the size of the likelihood ratio statistic in small samples, although these corrections are not the ultimate panacea.