Theories of public policy change, despite their differences, converge on one point of strong agreement: the relationship between policy and its causes can and does change over time. This consensus yields numerous empirical implications, but our standard analytical tools are inadequate for testing them. As a result, the dynamic and transformative relationships predicted by policy theories have been left largely unexplored in time series analysis of public policy. This article introduces dynamic linear modelling (DLM) as a useful statistical tool for exploring time-varying relationships in public policy. The article offers a detailed exposition of the DLM approach and illustrates its usefulness with a time series analysis of United States defense policy from 1957 to 2010. The results point the way for a new attention to dynamics in the policy process, and the article concludes with a discussion of how this research programme can profit from applying DLMs.