Behavior initiation is a form of leadership and is an important aspect of social organization that affects the processes of group formation, dynamics, and decision-making in human societies and other social animal species. In this work, we formalize the "Coordination Initiator Inference Problem" and propose a simple yet powerful framework for extracting periods of coordinated activity and determining individuals who initiated this coordination, based solely on the activity of individuals within a group during those periods. The proposed approach, given arbitrary individual time series, automatically (1) identifies times of coordinated group activity, (2) determines the identities of initiators of those activities, and (3) classifies the likely mechanism by which the group coordination occurred, all of which are novel computational tasks. We demonstrate our framework on both simulated and real-world data: trajectories tracking of animals as well as stock market data. Our method is competitive with existing global leadership inference methods but provides the first approaches for local leadership and coordination mechanism classification. Our results are consistent with ground-truthed biological data and the framework finds many known events in financial data which are not otherwise reflected in the aggregate NASDAQ index. Our method is easily generalizable to any coordinated time-series data from interacting entities.