Unit root tests based on adaptive maximum likelihood estimation

Adaptive maximum likelihood estimators of unit roots in autoregressive proc esses with possibly non-Gaussian innovations are considered. Unit root test s based on the adaptive estimators are constructed. Limiting distributions of the test statistics are derived, which are linear combinations of two fu nctionals of Brownian motions. A Monte Carlo simulation reveals that the pr oposed tests have improved powers over the classical Dickey-Fuller tests wh en the distribution of the innovation is not close to normal. We also compa re the proposed tests with those of Lucas (1995, Econometric Theory 11, 331 -346) based on M-estimators.