Exact Inference in Predictive Quantile Regressions with an Application to Stock Returns

We develop an exact and distribution-free procedure to test for quantile predictability at several quantile levels jointly, while allowing for an endogenous predictive regressor with any degree of persistence. The approach proceeds by combining together the quantile regression t-statistics from each considered quantile level and uses Monte Carlo resampling techniques to control the overall significance level of the data-dependent combination in finite samples. A simulation study confirms the fact that the proposed inference procedure controls the familywise error rate and achieves good power. We use the new approach to test the ability of many commonly used variables to predict the quantiles of excess stock returns, and shed new light on tail predictability.