SGER: Statistics of Extremes, with Applications in Financial Time Series

Washington University, Saint Louis MO

Investigators

Abstract

The proposal pursues a series of developments of new test statistics for tail independence and of new measures for tail dependence. Particularly, the investigator studies extreme correlation coefficient, tail dependence measures, gamma test statistics. These are related to the study of statistics of multivariate extremes. In financial applications, the proposal will also specify new models for asset pricing and extreme co-movements for market data, and develop new portfolio evaluation tools more sensitive to these co-movements. A new measure for extreme co-movement is introduced. The proposal includes the development of statistical estimation methods for max-stable processes. Procedures of how to calculate portfolio risk measures are also introduced using combined Markov process and max-stable process models. As all definitions used for extremal dependence depend on some limit procedures and often concern statistical testing for parameters at the edge of a specific parametric space, great care has to be taken to obtain tests with sufficient power. The proposal is exactly aiming at finding a solution for this. The investigator will carefully compare and contrast new approaches with existing ones using simulated as well as real data. The real data will come from areas as diverse as insurance, finance, telecommunications, climatology, seismology, medicine, etc. Throughout applications in diverse fields (like above), extreme risks play an important scientific, societal as well as (possibly) political role. The dissemination of new statistical tools leading to a better understanding of the occurrence of joint extremes is of great importance. This can be very well achieved at the level of new graduate courses, publications in journals aimed at a broaden audience and in discussion with scientists from other fields.