We introduce a framework for causal discovery and attribution of causal influence for rare events in time series data--where the interest is in identifying causal links and root causes of individual discrete events rather than the types of these events. Specifically, we build on the theory of temporal point processes, and describe a discrete-time analogue of Hawkes processes to model the occurrence of self-exciting rare events with instantaneous effects. We then introduce several scores to measure causal influence among individual events. These statistics are drawn from causal inference and temporal point process theories, describe complementary aspects of causality in temporal event data, and obey commonly used axioms for feature attribution. We demonstrate the efficacy of our model and the proposed influence scores on real and synthetic data.