Forecasting Tail Risk with Expectile Regression

This study proposes a novel expectile regression complete subset averaging (ECSA) method to forecast the downside risk for asset returns. Given a high-dimensional set of covariates, we combine the forecasts from a complete subset of expectile regression models that use a fixed number of regressors. The ECSA method is adaptable to weakly dependent data. All candidate models are allowed to be potentially misspecified, and the number of parameters can increase with the sample size. We obtain the optimal subset size by minimizing a leave-one-out cross-validation criterion. The consistency and asymptotic normality of the expectile regression estimator are well established. We also show the asymptotic optimality of the proposed ECSA estimator in terms of minimizing the out-of-sample final prediction error loss in a class of model averaging estimators. Monte Carlo simulations and an empirical application on the U.S. stock market returns demonstrate the superior performance of the proposed estimator compared with other competing model averaging and model selection methods