In this paper, we analyze the extreme events of non-stationary time series in the framework of horizontal visibility graph (HVG). We give a new definition of extreme events, which incorporates the temporal structure of the series and the degree of the nodes in the HVG. An advantage of the new concept is that it does not require ad hoc treatment even when the non-stationarity arises in time series. We also use the information-theoretic methods to analyze the degree of nodes in the HVG. In the numerical analysis, we study the statistical characterizations of the extreme events of synthetic time series, including the random noises, periodic time series, random walk processes, and the long-range auto-correlated time series. Then, we study 9 time series in stock markets to identify the extreme events evolving in these non-stationary systems. Interestingly, we find that the daily closing price series perform rather close to the random walk processes, while the daily trading volume series behave quite similar to the random noises.

中文翻译：

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使用水平能见度图的非平稳时间序列的极端事件分析

在本文中，我们在水平可见性图（HVG）的框架下分析了非平稳时间序列的极端事件。我们给出了极端事件的新定义，它结合了序列的时间结构和 HVG 中节点的度数。新概念的一个优点是即使在时间序列中出现非平稳性时也不需要临时处理。我们还使用信息论方法来分析 HVG 中节点的程度。在数值分析中，我们研究了合成时间序列的极端事件的统计特征，包括随机噪声、周期性时间序列、随机游走过程和长程自相关时间序列。然后，我们研究股票市场中的 9 个时间序列，以确定在这些非平稳系统中演变的极端事件。