  We introduce a method to infer lead-lag networks of agents' actions in
complex systems. These networks open the way to both microscopic and
macroscopic states prediction in such systems. We apply this method to
trader-resolved data in the foreign exchange market. We show that these
networks are remarkably persistent, which explains why and how order flow
prediction is possible from trader-resolved data. In addition, if traders'
actions depend on past prices, the evolution of the average price paid by
traders may also be predictable. Using random forests, we verify that the
predictability of both the sign of order flow and the direction of average
transaction price is strong for retail investors at an hourly time scale, which
is of great relevance to brokers and order matching engines. Finally, we argue
that the existence of trader lead-lag networks explains in a self-referential
way why a given trader becomes active, which is in line with the fact that most
trading activity has an endogenous origin.
