Testing for predictability of asset returns has been a long history in economics and finance. Recently, based on a simple predictive regression, Kostakis, Magdalinos and Stamatogiannis (2015, Review of Financial Studies) derived a Wald type test based on the context of the extended instrumental variable (IVX) methodology for testing predictability of stock returns and Demetrescu (2014) showed that the local power of the standard IVX-based test could be improved in some cases when a lagged predicted variable is added to the predictive regression on purpose, which poses a general important question on whether a lagged predicted variable should be included in the model or not. This paper proposes novel robust procedures for testing both the existence of a lagged predicted variable and the predictability of asset returns in a predictive regression regardless of regressors being stationary or nearly integrated or unit root. A simulation study confirms the good finite sample performance of the proposed tests. We further apply the proposed tests to some real datasets in finance to illustrate their usefulness in practice.