Lithuanian Mathematical Journal

, Volume 59, Issue 4, pp 545–574 | Cite as

Risk forecasting in the context of time series*

  • Xiaoyang LuEmail author
  • Gennady Samorodnitsky


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.


heavy tails regular variation 


primary 60E05 91B30 secondary 60G70 


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© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of Operations Research and Information EngineeringCornell UniversityIthacaUSA

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