Three emerging applications are driving a renewed interest in vector point processes: neural coding, high frequency finance and genomics. This pressure has revealed a gross lack of models and system identification methods. In particular in at least the first two applications coincidences can occur i.e. more than one event can occur at the same time. Yet the models in common use exclude this possibility. In this paper we develop a class of time-varying vector Poisson models that allow coincident events and develop for the first time an hypothesis test for no coincidences. We show simulation results and an application to high frequency finance data.