Despite the fact that it is not correct to speak of Bartlett corrections in
the case of nonstationary time series, this paper shows that a Bartlett-ty
pe correction to the likelihood ratio test for a unit root can he an effect
ive tool to control size distortions. Using well-known formulae, we obtain
second-order (numerical) approximations to the moments and cumulants of the
likelihood ratio, which makes it possible to calculate a Bartlett-type fac
tor. It turns out that the cumulants of the corrected statistic are closer
to their asymptotic value than the original one. A simulation study is then
carried out to assess the quality of these approximations for the first fo
ur moments; the size and the power of the original and the corrected statis
tic are also simulated. Our results suggest that the proposed correction re
duces the size distortion without affecting the power too much.