The test for stationarity versus trends and unit roots for a wide class of dependent errors

We suggest a rescaled variance type of test for the null hypothesis of stationarity against deterministic and stochastic trends (unit roots). The deterministic trend can be represented as a general function of time (e.g. non-parametric, linear or polynomial regression, abrupt changes in the mean). Under the null, the asymptotic distribution of the test is derived and critical values are tabulated for a wide class of stationary processes with short, long or negative dependence structure. A simulation study examines the performance of the test in terms of size and power. The empirical performance of the test is illustrated using the S&P 500 data.