This paper studies likelihood-based estimation and tests for autoregressive time series models with deterministic trends and general disturbance distributions. In particular, a joint estimation of the trend coefficients and the autoregressive parameter is considered. Asymptotic analysis on the M-estimators is provided. It is shown that the limiting distributions of these estimators involve nonlinear equation systems of Brownian motions even for the simple case of least squares regression. Unit root tests based on M-estimation are also considered, and extensions of the Neyman–Pearson test are studied. The finite sample performance of these estimators and testing procedures is examined by Monte Carlo experiments.