AI 中文总结
针对期望短缺（ES）预测的不可识别性与模型不确定性问题，提出两阶段交叉验证模型平均方法，经理论验证及模拟、实证分析，该方法预测准确稳定且计算高效。
AI 中文摘要
期望短缺（ES）被广泛用于衡量金融和经济学中的尾部风险，但由于其不可识别性和模型不确定性，对其进行预测颇具挑战性。本文提出一种用于ES预测的两阶段交叉验证模型平均方法：第一阶段采用分位数模型平均估计条件风险价值；第二阶段构建转换后的响应，并应用基于均方误差的模型平均来估计ES。我们在模型设定正确和模型误设两种情况下建立了所提方法的理论性质，证明了估计量的一致性和预测风险的渐近最优性。模拟研究以及对美国股票收益率和宏观经济GDP增长数据的实证应用表明，该方法能提供准确、稳定的ES预测，且计算效率高。
英文摘要
Expected shortfall (ES) is widely used to measure tail risk in finance and economics, but its prediction is challenging due to non-elicitability and model uncertainty. This paper proposes a two-stage cross-validation model averaging method for ES forecasting. In the first stage, conditional value-at-risk is estimated using quantile model averaging. In the second stage, a transformed response is constructed and mean squared error-based model averaging is applied to estimate ES. We establish theoretical properties of the proposed method under both correct specification and model misspecification, showing consistency of the estimators and asymptotic optimality of the forecasting risk. Simulation studies and empirical applications to U.S. stock return and macroeconomic GDP growth data show that the proposed approach provides accurate and stable ES forecasts and is computationally efficient.
