Likelihood-based inference in trending time series with a root near unity

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