We review theory and methodology of the class of simultaneous graphical dynamic linear models (SGDLMs) that provide flexibility, parsimony and scalability of multivariate time series analysis. Discussion includes core theoretical aspects and summaries of existing Bayesian methodology for forward filtering and forecasting with SGDLMs. The review is complemented by new theory linking dynamic graphical and factor models, and extensions of the Bayesian methodology. This addresses graphical structure uncertainty via model marginal likelihood evaluation, and analysis with missing data relevant to counterfactual analysis. The latter advances the ability to scale causal analysis to higher-dimensional time series. Aspects of the theory and methodology are exemplified in a global macroeconomic time series study with time-varying cross-series relationships and primary interests in potential causal effects. The example highlights the utility of SGDLMs with insights generated by the theoretical structure of these models, and benefits of fully Bayesian assessment of post-intervention outcomes in causal time series studies as in prediction more generally.
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