Bartlett corrections are derived for testing hypotheses
about the autoregressive parameter
ρ 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 ρ. In
the models with deterministic terms, the correction
factor is asymmetric in ρ.
Furthermore, the Bartlett correction is
monotonically 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 likelihood ratio
statistic in small samples, although these
corrections are not the ultimate panacea.