Extremal Dependence of Time Series
Holger Drees
University of Hamburg
By now the statistical analysis of independent extreme risks is well
developed. In contrast, the understanding of the statistical
inference on the dependence between extreme events over time is
rather patchy, despite the fact that the total risk is often
strongly influenced by the clustering behaviour of extremal events.
For example, the risk of huge accumulated losses in a financial
investment is larger if days with large losses tend to occur in
clusters.
We present a systematic approach to the analysis of the extremal
serial dependence of such time series using empirical process
theory. Particular attention is turned to the bias which is known to
often cause serious misjudgment of the clustering behaviour and hence
of the total risk.