Identifying exogenous and endogenous activity in social media

The occurrence of new events in a system is typically driven by external
causes and by previous events taking place inside the system. This is a general
statement, applying to a range of situations including, more recently, to the
activity of users in Online social networks (OSNs). Here we develop a method
for extracting from a series of posting times the relative contributions of
exogenous, e.g. news media, and endogenous, e.g. information cascade. The
method is based on the fitting of a generalized linear model (GLM) equipped
with a self-excitation mechanism. We test the method with synthetic data
generated by a nonlinear Hawkes process, and apply it to a real time series of
tweets with a given hashtag. In the empirical dataset, the estimated
contributions of exogenous and endogenous volumes are close to the amounts of
original tweets and retweets respectively. We conclude by discussing the
possible applications of the method, for instance in online marketing.