We investigate a test for unit roots in autoregressive time series based on maximization of the unconditional likelihood. This is the likelihood function appropriate for stationary time series. While this function is the true likelihood only under the stationary alternative, it can nevertheless be maximized for any data including data from a unit root process. It thus gives a way to test for unit roots, provided percentill~s can be calculated. For models with estimated means, the power of the new test is better than that of some currently popular tests
