Exact Inference in Long-Horizon Predictive Quantile Regressions with an Application to Stock Returns*

We develop an exact and distribution-free procedure to test for quantile predictability at several prediction horizons and 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 prediction horizon and quantile level, and uses Monte-Carlo resampling techniques to control the familywise error rate in finite samples. A simulation study confirms that the proposed inference procedure is indeed level-correct and that testing several quantile levels jointly can deliver more power to detect predictability. In an empirical application to excess stock returns, we find that the default yield spread predicts the right tail while the short-term interest rate predicts the center of the return distribution. This predictability evidence is stronger at shorter rather than longer horizons.