Hate speech is ubiquitous on the Web. Recently, the offline causes that contribute to online hate speech have received increasing attention. A recurring question is whether the occurrence of extreme events offline systematically triggers bursts of hate speech online, indicated by peaks in the volume of hateful social media posts. Formally, this question translates into measuring the association between a sparse event series and a time series. We propose a novel statistical methodology to measure, test and visualize the systematic association between rare events and peaks in a time series. In contrast to previous methods for causal inference or independence tests on time series, our approach focuses only on the timing of events and peaks and no other distributional characteristics. We follow the framework of event coincidence analysis (ECA) that was originally developed to correlate point processes. We formulate a discrete-time variant of ECA and derive all required distributions to enable analyses of peaks in time series with a special focus on serial dependencies and peaks over multiple thresholds. The analysis gives rise to a novel visualization of the association via quantile-trigger rate plots. We demonstrate the utility of our approach by analyzing whether Islamist terrorist attacks in Western Europe and North America systematically trigger bursts of hate speech and counter-hate speech on Twitter.

中文翻译：

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恐怖主义会触发在线仇恨言论吗？关于事件与时间序列的关联

仇恨言论在网络上无处不在。近来，导致在线仇恨言论的离线原因越来越受到关注。一个反复出现的问题是，离线发生的极端事件是否会系统性地触发在线的仇恨言论爆发，这是由仇恨社交媒体帖子数量的高峰所表明的。形式上，这个问题转化为衡量稀疏事件序列和时间序列之间的关联。我们提出了一种新颖的统计方法来测量，测试和可视化时间序列中的稀有事件和峰值之间的系统关联。与以前对时间序列进行因果推理或独立性测试的方法相比，我们的方法仅关注时序事件和峰值，没有其他分布特征。我们遵循最初用于关联点过程的事件一致性分析（ECA）框架。我们制定了ECA的离散时间变体，并导出了所有必需的分布，以能够对时间序列中的峰进行分析，并特别关注序列依赖性和多个阈值上的峰。通过分位数触发速率图，分析产生了一种新颖的关联可视化。通过分析西欧和北美的伊斯兰恐怖袭击是否系统地触发Twitter上的仇恨言论和反仇恨言论的爆发，我们证明了我们方法的实用性。