Regime-specific Return Predictability in Quantiles

This paper captures the underlying regime switching mechanism in the prediction of stock returns via a predictive quantile regression with multiple thresholds. The predictability of each predictor is allowed to switch from one regime to another according to the value of a threshold variable and could vary across quantiles, and the predictors could possess heterogeneous degrees of persistence. Statistical learning techniques, including a sequential estimation procedure, an adaptive group Lasso refinement and a backward elimination algorithm, are adopted to estimate the unknown multiple thresholds. The adaptive Lasso is then applied to identify the important predictors in each regime to improve prediction accuracy at each quantile. Asymptotic properties of the proposed estimators are established, which are further corroborated with their nice finite sample performance revealed in simulations. The empirical analysis for the U.S. stock returns shows that the return predictability of several predictors changes with the economic states across the quantiles, demonstrating the regime-specific return predictability in quantiles.