This article presents a general statistical approach suitable for the analysis of time-resolved (time-series) cross-cultural data. The goal is to test theories about the evolutionary processes that generate cultural change. This approach allows us to investigate the effects of predictor variables (proxying for theory-suggested mechanisms), while controlling for spatial diffusion and autocorrelations due to shared cultural history (known as Galton’s Problem). It also fits autoregressive terms to account for serial correlations in the data and tests for nonlinear effects. I illustrate these ideas and methods with an analysis of processes that may influence the evolution of one component of social complexity, information systems, using the Seshat: Global History Databank.