Ordinal Patterns in clusters of extremes of regulary varying time series

The purpose is to investigate temporal clusters of extremes defined as subsequent exceedances of high thresholds in a stationary time series. Two meaningful features of these clusters are the probability distribution of the cluster size and the ordinal patterns within a cluster. The latter have been introduced in order to handle data sets with several thousand data points appearing in medicine, biology, finance and computer science. Since these patterns take only the ordinal structure of consecutive data points into account, the method is robust under monotone transformations and measurement errors. We verify the existence of the corresponding limit distributions in the framework of regularly varying time series, develop non-parametric estimators and show and their asymptotic normality under appropriate mixing conditions.