We present a new decomposition of transfer entropy to characterize the degree of synergy- and redundancy-dominated influence a time series has upon the interaction between other time series. We prove the existence of a class of time series, where the early past of the conditioning time series yields a synergistic effect upon the interaction, whereas the late past has a redundancy-dominated effect. In general, different parts of the past can have different effects. Our information theoretic quantities are easy to compute in practice, and we demonstrate their usage on real-world brain data.