(corresponding to the 11 weeks before and 1 week after the event, but a year earlier);

the observed series 23 weeks prior to the event, similarly for 12 week;[^10] and

external information from Twitter, Reddit, and news sources.

The external information includes time series whose behavior is unlikely to be affected by the events (§\[sec:analysis\]). First, we use the overall volume of news on GDELT (i.e., number of daily news article URLs per day) as it does not seem to be affected by any of our events during the observation window. Second, we use the overall number of tweets containing the word “news” which we also observe is not affected by any of our events (also a proxy for the overall volume of tweets). Third, we use the overall number of Reddit posts containing the general term “people,” which we also observe is not affected by the events in our list (this is not the case for the series of posts in Reddit containing, e.g., the term “breaking news” which was affected by several of our events).

The methodology for synthesizing the control follows @brodersen2015inferring, using a state space model to predict the counterfactual from the various sources we described 