Theory of Probability &Its Applications, Volume 66, Issue 4, Page 729-741, February 2022.
Based on the law of large numbers and the central limit theorem under nonlinear expectation, we introduce a new method of using ${G}$-normal distribution to measure financial risks. Applying max-mean estimators and a small windows method, we establish autoregressive models to determine the parameters of ${G}$-normal distribution, i.e., the return, maximal, and minimal volatilities of the time series. Utilizing the value at risk (VaR) predictor model under ${G}$-normal distribution, we show that the ${G}$-VaR model gives an excellent performance in predicting the VaR for a benchmark dataset comparing to many well-known VaR predictors.

中文翻译：

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用 $G$-Expectation 衡量的金融时间序列的分布不确定性

概率论及其应用，第 66 卷，第 4 期，第 729-741 页，2022 年 2 月
。基于大数定律和非线性期望下的中心极限定理，我们介绍了一种使用 ${G}$-normal 的新方法分布以衡量金融风险。应用最大均值估计器和小窗口方法，我们建立自回归模型来确定${G}$-正态分布的参数，即时间序列的收益、最大和最小波动率。利用 ${G}$-正态分布下的风险价值 (VaR) 预测模型，我们表明 ${G}$-VaR 模型在预测基准数据集的 VaR 方面与许多知名的VaR 预测因子。