Previous literature indicates that stock returns are predictable by several strongly autocorrelated forecasting variables, especially at longer horizons. It is suggested that this finding is spurious and follows from a neglected near unit root problem. Instead of the commonly used t-test, we propose a test that can be considered as a general test of whether the return can be predicted by any highly persistent variable. Using this test, no predictability is found for U.S. stock return data from the period 1928-1996. Simulation experiments show that the standard t-test clearly overrejects whereas our proposed test controls size much better.