OPTIMAL MODEL AVERAGING FOR JOINT VALUE-AT-RISK AND EXPECTED SHORTFALL REGRESSION
针对巴塞尔协议III中预期亏损与风险价值的联合建模问题，提出一种通过刀切法选择权重向量的模型平均方法，并证明其大样本性质和渐近最优性，模拟和实证表现良好。
Since the implementation of the Basel III Accord, expected shortfall (ES) has gained increasing attention from regulators as a complement to value-at-risk (VaR). The problem of elicitability for ES makes jointly modeling VaR and ES a popular method to study ES. In this article, we develop model averaging for joint VaR and ES regression models that selects the two weight vectors by minimizing a jackknife criterion. We show the large sample properties of the estimators under potential model misspecification with increasing dimension of parameters and the asymptotic optimality of the selected weights in the sense of minimizing the out-of-sample excess final prediction error. Simulation studies and three empirical analyses reveal good finite sample performance.