Out-of-sample equity premium predictability and sample split-invariant inference

For a comprehensive set of 21 equity premium predictors we find extreme variation in out-of-sample predictability results depending on the choice of the sample split date. To resolve this issue we propose reporting in graphical form the out-of-sample predictability criteria for every possible sample split, and two out-of-sample tests that are invariant to the sample split choice. We provide Monte Carlo evidence that our bootstrap-based inference is valid. The in-sample, and the sample split invariant out-of-sample mean and maximum tests that we propose, are in broad agreement. Finally we demonstrate how one can construct sample split invariant out-of-sample predictability tests that simultaneously control for data mining across many variables.