Penalized Optimal Forecast Combination for Quantile Regressions

This paper develops a novel forecast combination approach for quantile regressions (QR) that accommodate both linear and nonlinear forms for parameters and regressors. We propose a penalized weight choice criterion based on the Kullback-Leibler loss in a quasi-likelihood framework that allows parameter uncertainty and model misspecification. This criterion simultaneously selects optimal combination weights and reduces model complexity, which covers special cases such as the Mallows-type criterion in linear QR. First, we prove the asymptotic optimality of the proposed combination method in diverging-dimensional settings for both linear and nonlinear QR cases. Second, we establish the consistency of the selected weights either for the misspecified and correctly specified candidate models, which complements existing model averaging literature for QR that only focuses on asymptotic optimality. Finally, we examine finite sample performance through Monte Carlo simulations and demonstrate advantages over existing methods via an empirical application to excess return forecasting.