In this paper, we 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 giving the relative positions of the data points within a cluster. 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 their asymptotic normality under appropriate mixing conditions. The performance of the estimators is demonstrated in a simulated example and a real data application to discharge data of the river Rhine.

在本文中，我们研究了极端的时间集群，这些集群被定义为固定时间序列中高阈值的后续超出。这些聚类的两个有意义的特征是聚类大小的概率分布和给出聚类内数据点相对位置的顺序模式。由于这些模式仅考虑连续数据点的序数结构，因此该方法在单调变换和测量误差下是可靠的。我们在规则变化的时间序列框架内验证了相应极限分布的存在，开发了非参数估计量并在适当的混合条件下显示了它们的渐近正态性。估算器的性能在一个模拟示例中得到了证明，并在实际数据应用程序中得到了莱茵河的数据。