On predicting stock returns with nearly integrated explanatory variables

Statistical inference in predictive regressions depends critically on the stochastic properties of the posited explanatory variable, in particular, its order of integration. Confidence intervals computed for the largest autoregressive root of many explanatory variables commonly used in predictive regressions, including the dividend yield, the book-to-market ratio, the short-term rate of interest, and the term and default spreads, confirm uncertainty surrounding these variables' order of integration. We investigate the effects of this uncertainty on inferences drawn in predictive regressions. Once this uncertainty is accounted for, contrary to previous evidence, we find reliable evidence of predictability at shorter rather than at longer horizons.