A correction factor for unit root test statistics

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-type correction to the likelihood ratio test for a unit root can he an effective 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 factor. 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 four moments; the size and the power of the original and the corrected statistic are also simulated. Our results suggest that the proposed correction reduces the size distortion without affecting the power too much.