Jackknife Model Averaging for Quantile Regressions

In this paper we consider the problem of frequentist model averaging for quantile regression (QR) when all the M models under investigation are potentially misspecified and the number of parameters in some or all models is diverging with the sample size n. To allow for the dependence between the error terms and the regressors in the QR models, we propose a jackknife model averaging (JMA) estimator which selects the weights by minimizing a leave-one-out cross-validation criterion function and demonstrate that the jackknife selected weight vector is asymptotically optimal in terms of minimizing the out-of-sample final prediction error among the given set of weight vectors. We conduct Monte Carlo simulations to demonstrate the finite-sample performance of the proposed JMA QR estimator and compare it with other model selection and averaging methods. We find that in terms of out-of-sample forecasting, the JMA QR estimator can achieve significant efficiency gains over the other methods, especially for extreme quantiles. We apply our JMA method to forecast quantiles of excess stock returns and wages.