Abstract
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.
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Dedicated to Vygantas Paulauskas, an inspiration and a friend
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*This research was partially supported by the ARO grants W911NF-12-10385 and W911NF-18 -10318 at Cornell University
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Lu, X., Samorodnitsky, G. Risk forecasting in the context of time series*. Lith Math J 59, 545–574 (2019). https://doi.org/10.1007/s10986-019-09467-4
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DOI: https://doi.org/10.1007/s10986-019-09467-4