We propose an approach for forecasting risk contained in future observations in a time series. We take into account both the shape parameter and the extremal index of the data. This significantly improves the quality of risk forecasting over methods that are designed for i.i.d. observations and over the return level approach. We prove functional joint asymptotic normality of the common estimators of the shape parameter and and extremal index estimators, based on which statistical properties of the proposed forecasting procedure can be analyzed.

中文翻译：

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时间序列背景下的风险预测*

我们提出了一种预测时间序列中未来观察中包含的风险的方法。我们同时考虑了数据的形状参数和极值索引。这显着提高了风险预测的质量，而不是为 iid 观察设计的方法和回报水平方法。我们证明了形状参数和极值指数估计量的共同估计量的函数联合渐近正态性，在此基础上可以分析所提出的预测程序的统计特性。