规则变化时间序列极值簇的有序模式
Ordinal Patterns in Clusters of Subsequent Extremes of Regularly Varying Time Series
摘要：
在本文中，我们研究的时间集群的极端定义为后续的高阈值在一个平稳时间序列的重复。这些聚类的两个有意义的特征是聚类大小的概率分布和聚类内的有序模式。由于这些模式只考虑了连续数据点的有序结构，因此该方法在单调变换和测量误差下具有鲁棒性。我们验证了相应的极限分布的存在性的框架下，定期变化的时间序列，开发非参数估计，并显示其渐近正态性在适当的混合条件。在模拟的例子和一个真实的数据应用程序，莱茵河的流量数据的估计器的性能。
英文摘要：
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 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.
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