Predictive Regressions Revisited

Statistical inference in predictive regressions depends critically on the stochastic properties of the posited explanatory variable, in particular, its order of integration. However, confidence intervals for the largest autoregressive root of explanatory variables commonly used in predictive regressions, including the dividend yield, the book-to-market ratio, and the term and default spreads, confirm uncertainty surrounding these variables’ order of integration. Using a local to unity framework we investigate the effects of uncertainty in an explanatory variable’s order of integration on inferences drawn in predictive regressions. We find no evidence that dividend yields or book-to-market ratios can predict one period ahead stock returns. In the case of predictive regressions using long horizon returns, statistical inference depends not only on the explanatory variable’s order of integration but also on the length of the horizon itself.