A causal inference revolution has been under way in political methodology for the better part of the last decade. Time series analysts have not been major contributors to this revolution because the tools that have been developed thus far do not fit our data. Existing methods either require analyst to pool observations so that analysts can differentiate treatment and control units, require analysts to identify or develop suitable control series, or require the analyst to exercise control over treatment in a time series experiment. Our goal is to identify the assumptions and conditions required for analysts to make causal inferences with observational time series data when observations cannot be pooled, control series are unavailable, and counterfactuals cannot be forecast. We highlight the critical assumptions for causal identification in structural dynamic systems: partial equilibrium recursivity and conditional exogeneity. We discuss the conditions when these assumptions are plausible, outline tests for conditional exogeneity and structural non-causality, and consider the potential limitations of the proposed framework. When the proposed assumptions are met, standard Granger non-causality tests provide a means for analysts to recover causal estimands.