• Prof. Martin Schlather – University of Gottingen – Germany
  • FCUL (DEIO) – Campo Grande – Bloco C/6 Piso 4 – Sala 6.4.31- 14h 30m
  • Quarta-feira, 12 de Março de 2008

Abstract: The extremal index has been an important quantity to characterize the extremal behaviour of a stationary time series. It can be seen as the probability of a run below some large threshold $u$ given the first value is larger than $u$. The extremal index has been extended to the multivariate extremal index function by Nandagopalan (1994). Also various modifications have been considered in meanwhile, e.g. functions of extremal indices based on clustering or thinning  (Robinson and Tawn, 2000). Related quantities that give further insight into the structure of the clusters are the upcrossing index by Ferreira (2006) or the extremal coefficient function.


In this talk, a short overview over quantities related to the extremal index is given. We then concentrate on the properties of the extremal index function and some relation to the extremal coefficient.