Statistics of Dependent Variables
Classical extreme value statistics is dominated by the theory for independent and identically distributed (iid) observations. In many applications, though, one encounters a non-negligible serial (or spatial) dependence. For instance, returns of an investment over successive periods are usually dependent, cf. Chapter 16, and stable low pressure systems can lead to extreme amounts of rainfall over several consecutive days. These examples demonstrate that a positive dependence between extreme events is often particularly troublesome as the consequences, which are already serious for each single event, may accumulate and finally result in a devastating catastrophe.
KeywordsDependence Structure Time Series Model Asymptotic Variance GARCH Model Extremal Index
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