  A unit root test is proposed for time series with a general nonlinear
deterministic trend component. It is shown that asymptotically the pooled OLS
estimator of overlapping blocks filters out any trend component that satisfies
some Lipschitz condition. Under both fixed-$b$ and small-$b$ block asymptotics,
the limiting distribution of the t-statistic for the unit root hypothesis is
derived. Nuisance parameter corrections provide heteroskedasticity-robust
tests, and serial correlation is accounted for by pre-whitening. A Monte Carlo
study that considers slowly varying trends yields both good size and improved
power results for the proposed tests when compared to conventional unit root
tests.
