Unified Tests for a Dynamic Predictive Regression

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 derived a Wald type test based on the context of the extended instrumental variable (IVX) methodology for testing predictability of stock returns, and Demetrescu showed that the local power of the standard IVX-based test could be improved for some range of alternative hypotheses and the tuning parameter when a lagged predicted variable is added to the predictive regression on purpose, which poses an important question on whether the predictive model should include a lagged predicted variable. This article proposes novel robust procedures for testing both the existence of a lagged predicted variable and the predictability of asset returns regardless of regressors being stationary or nearly integrated or unit root and the AR model for regressors with or without an intercept. A simulation study confirms the good finite sample performance of the proposed tests before illustrating their practical usefulness in analyzing real financial datasets.