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

We suggest a rescaled variance type test for stationarity (null hypothesis) against deterministic trends and unit roots. The asymptotic (parameter free) distribution of the test is derived and critical values tabulated by simulations for a wide class of stationary errors with short, long or negative dependence structure. The proposed test detects a deterministic trend that can be presented as a general function in time, for example non-parametric, linear or polynomial regression, abrupt changes in the mean plus unobserved stationary error process which has an unspecified short, long or negative memory dependence structure. The test is also applicable for unit root models with/without deterministic trend. The simulations show that the power of the test significantly improves by increasing the number of observations allowing to detect changes in the mean under short and long memory errors.