Clustering of extreme events

schedule le lundi 06 juillet 2020 de 17h00 à 18h00

Organisé par : F. Bechtold, W. Da Silva , A. Fermanian, S. Has, Y. Yu

Intervenant : Gloria Buritica (LPSM)
Lieu : Online at https://bigbluebutton.math.upmc.fr/b/ade-phf-9dg

Sujet : Clustering of extreme events

Résumé :

The occurrence of an extreme event usually triggers a sequence of extreme events in a short period. In practice, this phenomenon enchains very negative consequences when the risk model does not account for the probability of time-clustering of extremes. For example, many floods occur after recording extreme rainfall data for consecutive days. Similarly, returns for stock prices crash for several days before returning to a usual dynamic. 

In the setting of regularly varying stationary time series, the extremal index is a parameter that fully describes in most cases the time-clustering of extremes for univariate time series. The multivariate setting inspires from these results and considers time-clusters as data from a portion of time with the supremum norm exceeding a high threshold. We study a generalisation of this notion considering time-blocks of data with norm Lp above a high threshold. This new definition allows for capturing extreme behavior from more time-blocks than before. 

Key-words : Extreme value theory,  time clustering, extremal index, heavy-tail distributions.