Extreme Value Theory: Clustering

This lecture discusses the extremal index, which measures the mean size of clusters of extremes in a sequence. It explores the D'(un) condition for short-range dependence in processes, and the implications for modeling extreme events. The lecture also covers the impact of clustering on return levels and the estimation of the extremal index. Point processes and cluster size distributions are defined, highlighting the properties of clusters and their distribution. Various conditions, such as D(un) and A'(un), are examined for their role in determining the limiting cluster process. The lecture concludes with a discussion on the statistical consequences of clustering and the models used for analyzing extremes in time series.