Penalized Model Averaging for High Dimensional Quantile Regressions

This paper proposes a new penalized model averaging method for high dimensional quantile regressions based on quasi-maximum likelihood estimation, which determines optimal combination weights and yields sparseness from various potential covariates simultaneously. The proposed weight choice criterion is based on the Kullback-Leibler loss with penalties, which could reduce to Mallows-type criterion for asymmetric Laplace density, and both the dimension of covariates and the number of possibly misspecified candidate models are allowed to be diverging with the sample size. Also, the asymptotic optimality and convergence rate of the selected weights are derived under time series framework, even when all candidate models are misspecified. We further extend our concern to the ultra-high dimensional scenarios and establish the corresponding asymptotic optimality. Simulation studies and empirical application to stock returns forecasting illustrate that the proposed method outperforms existing methods.