Consider two stationary time series with heavy-tailed marginal distributions. We aim to detect whether they have a causal relation, that is, if a change in one causes a change in the other. Usual methods for causal discovery are not well suited if the causal mechanisms only appear during extreme events. We propose a framework to detect a causal structure from the extremes of time series, providing a new tool to extract causal information from extreme events. We introduce the causal tail coefficient for time series, which can identify asymmetrical causal relations between extreme events under certain assumptions. This method can handle nonlinear relations and latent variables. Moreover, we mention how our method can help estimate a typical time difference between extreme events. Our methodology is especially well suited for large sample sizes, and we show the performance on the simulations. Finally, we apply our method to real-world space-weather and hydro-meteorological datasets.

翻译：考虑两个具有重尾边缘分布的平稳时间序列。我们旨在检测它们之间是否存在因果关系，即一个序列的变化是否引起另一个序列的变化。当因果机制仅在极值事件中出现时，常用的因果发现方法并不适用。我们提出一个从时间序列极值中检测因果结构的框架，为从极值事件中提取因果信息提供新工具。我们引入时间序列的因果尾部系数，该系数可在特定假设下识别极值事件之间的非对称因果关系。该方法能够处理非线性关系和潜在变量。此外，我们提及该方法如何有助于估计极值事件之间的典型时间差。我们的方法尤其适用于大样本量，并通过模拟实验展示了其性能。最后，我们将该方法应用于真实的空间天气与水文气象数据集。