Abstract. The identification of recurrences at various time scales in extreme event-like time series is challenging because of the rare occurrence of events which are separated by large temporal gaps. Most of the existing time series analysis techniques cannot be used to analyse extreme event-like time series in its unaltered form. The study of the system dynamics by reconstruction of the phase space using the standard delay embedding method is not directly applicable to event-like time series as it assumes a Euclidean notion of distance between states in the phase space. The edit distance method is a novel approach that uses the point-process nature of events. We propose a modification of edit distance to analyze the dynamics of extreme event-like time series by incorporating a nonlinear function which takes into account the sparse distribution of extreme events and utilizes the physical significance of their temporal pattern. We apply the modified edit distance method to event-like data generated from point process as well as flood event series constructed from discharge data of the Mississippi River in USA, and compute their recurrence plots. From the recurrence analysis, we are able to quantify the deterministic properties of extreme event-like data. We also show that there is a significant serial dependency in the flood time series by using the random shuffle surrogate method.

中文翻译：

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极端事件之类数据的重复分析

摘要。由于极少发生由大的时间间隔分隔的事件，因此在极端事件式时间序列中的各个时间尺度上重复发生的识别具有挑战性。大多数现有的时间序列分析技术不能用于以不变的形式分析类似于极端事件的时间序列。通过使用标准延迟嵌入方法重建相空间来研究系统动力学，因为它假设相空间中状态之间的距离是欧几里得概念，因此不适用于类事件时间序列。该编辑距离方法是一种利用事件的点过程性质的新颖方法。我们提出了一种修改编辑距离的方法，以通过结合非线性函数来分析类似于极端事件的时间序列的动力学，该非线性函数考虑了极端事件的稀疏分布并利用了其时间模式的物理意义。我们将改进的编辑距离方法应用于从点过程生成的类似事件的数据以及根据美国密西西比河的流量数据构建的洪水事件序列，并计算其重复图。从递归分析中，我们能够量化极端事件式数据的确定性。我们还表明，通过使用随机混洗替代方法，洪水时间序列中存在显着的序列依赖性。