A Unified Inference for Predictive Quantile Regression

The asymptotic behavior of quantile regression inference becomes dramatically different when it involves a persistent predictor with zero or nonzero intercept. Distinguishing various properties of a predictor is empirically challenging. In this paper, we develop a unified predictability test for quantile regression regardless of the presence of intercept and persistence of a predictor. The developed test is a novel combination of data splitting, weighted inference, and a random weighted bootstrap method. Monte Carlo simulations show that the new approach displays significantly better size and power performance than other competing methods in various scenarios, particularly when the predictive regressor contains a nonzero intercept. In an empirical application, we revisit the quantile predictability of the monthly S&P 500 returns between 1980 and 2019.