  The contagion dynamics can emerge in social networks when repeated activation
is allowed. An interesting example of this phenomenon is retweet cascades where
users allow to re-share content posted by other people with public accounts. To
model this type of behaviour we use a Hawkes self-exciting process. To do it
properly though one needs to calibrate model under consideration. The main goal
of this paper is to construct moments method of estimation of this model. The
key step is based on identifying of a generator of a Hawkes process. We perform
numerical analysis on real data as well.
