This paper makes use of the novel Generalized Stochastic Unit Root (GSTUR) model, Bayesian model estimation and model comparison techniques to investigate the presence of a deterministic time trend in economic series. The model is specified to allow for changes in persistence over time, such as shifts from stationarity I(0) to nonstationarity I(1) or vice versa. This uncertainty raises the crucial question about how sure one can be that an economic time series has a deterministic trend when there is a change in the underlying properties. Empirical analysis indicates that the GSTUR model could provide new insights on time series studies.