Forecasting Expected Shortfall a

读一篇：
Forecasting Expected Shortfall and Value-at-Risk with the FZ Loss and Realized Variance Measures
使用 FZ 损失和已实现方差度量来预测预期缺口和风险价值

Abstract
Low-frequency risk measures can filter out noise and better reflect the trend. In order to improve the forecasting accuracy of low-frequency risk through making full use of the valuable information contained in high-frequency independent variables, we propose a novel joint elicitable mixed data sampling (JE-MIDAS) model by introducing MIDAS method into JE regression model. We utilize the JE-MIDAS model to forecast value at risk and expected shortfall simultaneously and compare its performance with that of other popular models through both the Monte Carlo simulations and real-world applications. The numerical results show that our model is superior to other models because it can model mixed-frequency data directly, which avoids the information loss caused by frequency conversion. The empirical results on three stock indices also show that market volatility can increase financial risk. Interest rate has positive effects on risks for U.S. S&P500 and U.K. FTSE, whereas negative for SHCI of China.
低频风险指标可以滤除噪音，更好地反映趋势。 为了充分利用高频自变量中包含的有价值的信息来提高低频风险的预测精度，将MIDAS方法引入JE回归中，提出了一种新颖的联合可导出混合数据采样（JE-MIDAS）模型 模型。 我们利用 JE-MIDAS 模型同时预测风险价值和预期缺口，并通过蒙特卡罗模拟和实际应用将其性能与其他流行模型的性能进行比较。 数值结果表明，我们的模型优于其他模型，因为它可以直接对混合频率数据进行建模，避免了频率转换带来的信息损失。 三个股指的实证结果也表明，市场波动会增加金融风险。 利率对美国标普500和英国富时的风险有正向影响，而对中国上证指数则有负向影响。