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Hate speech is ubiquitous on the Web. Recently, the offline causes thatcontribute to online hate speech have received increasing attention. Arecurring question is whether the occurrence of extreme events offlinesystematically triggers bursts of hate speech online, indicated by peaks in thevolume of hateful social media posts. Formally, this question translates intomeasuring the association between a sparse event series and a time series. Wepropose a novel statistical methodology to measure, test and visualize thesystematic association between rare events and peaks in a time series. Incontrast to previous methods for causal inference or independence tests on timeseries, our approach focuses only on the timing of events and peaks, and noother distributional characteristics. We follow the framework of eventcoincidence analysis (ECA) that was originally developed to correlate pointprocesses. We formulate a discrete-time variant of ECA and derive all requireddistributions to enable analyses of peaks in time series, with a special focuson serial dependencies and peaks over multiple thresholds. The analysis givesrise to a novel visualization of the association via quantile-trigger rateplots. We demonstrate the utility of our approach by analyzing whether Islamistterrorist attacks in Western Europe and North America systematically triggerbursts of hate speech and counter-hate speech on Twitter.

Does Terrorism Trigger Online Hate Speech? On the Association of Events and Time Series