counterfactual of the treated time series, this is a generalization of the application of the differences-in-differences techniques to time series [@brodersen2015inferring].

![image](timelines-twitter-reddit-updated.pdf){width="98.00000%"}

[**Observed Time Series.** ]{} We consider time series covering our 19-month observation period with a granularity of one day. For each of the 825 terms we have for Twitter, we experiment with three time series: one for the number of tweets, one for the number of tweets excluding re-tweets (i.e., unique after removal of “RT @user” prefixes), and one for the number of unique users. Similarly, for the 1,257 terms we have for Reddit, we experiment with three time series: one for the number of posts, one for the total number of comments in these posts, and one for the total number of unique users in the post and comments.

[**Synthetic Control Time Series.** ]{} A synthetic control time series is a *counterfactual* that reflects behavior *had the extremist violence event not taken place*. For each treated time series, we build a control series for 1 week following the event based on several data sources:[^9]

the observed series in the 11 weeks leading to the event;

the observed series exactly 1 year before the event, for 12 weeks 