# Probability and Statistics Seminar

### Modelling extremal temporal dependence in stationary time series

Extreme value theory concerns the statistical study of the extremal properties of random processes. The most common problems treated by extreme value methods involve modeling the tail of an unknown distribution function from a set of observed data with the purpose of quantifying the frequency and severity of events more extreme than any that have been observed previously. A fundamental issue in applied multivariate extreme value (MEV) analysis is modelling dependence within joint tail regions. In this seminar we suggest modelling joint tails of the distribution of two consecutive pairs $(X_i;X_{i+1})$ of a first-order stationary Markov chain by a dependence model described in Ramos and Ledford (2009). Applications of this modelling approach to real data are then considered.

Ramos and Ledford (2009). A new class of models for bivariate joint tails. J. R. Statist. Soc., B. 71. p. 219-241.