Bayesian Dynamic Modeling of Multivariate Time Series

Abstract

Simultaneous graphical dynamic linear models provide advances in flexibility, parsimony, and scalability of multivariate time series analysis. Core theoretical aspects of such models are developed throughout this dissertation. These advances include new results based on spectral graph theory that demonstrate a correspondence between the structure of dynamic graphical models and latent factor models, which so far have been typically viewed as mutually exclusive. We also develop a new Monte Carlo algorithm for Bayesian model marginal likelihood evaluation that leverages the model's structure to improve sampling efficiency. Another Monte Carlo approach is developed for sequentially sampling missing data. This development allows for counterfactual inference, enhancing Bayesian causal analyses of time series data. A backward sampling algorithm allows for retrospective inference in general, with special attention given to causal implications.The framework advances the ability to scale causal analysis to higher-dimensional time series. Methodological developments are demonstrated throughout using a global macroeconomic time series with time-varying cross-series relationships and primary interests in potential causal effects. The new methods for marginal likelihood evaluation enable model averaging to account for uncertainty in the model's graphical structure. The results highlight the utility of the new methodology and insights generated by the theoretical structure of these models, and the benefits of the resulting fully Bayesian assessment of post-intervention outcomes in causal time series studies. A case study of the effect of the Affordable Care Act's Medicaid expansion on employment rates exemplifies the utility of this framework in contexts where treatment adoption is staggered in time. It further shows the benefit of jointly modeling the full multivariate time series for causal analysis, especially with respect to estimating average treatment effects. A final chapter builds a dynamic Bayesian model of the structure of Americans' political views, drawing on data from 1984 to 2022. Although extensive past work has used survey data to examine changes in the ideological consistency of the public's positions, very few studies have accounted for the time series nature of the data. Our analysis indicates that Americans' views across issues are more strongly correlated now than in the 1980s, but correlations between many issue pairs remain weak. An implied empirical factor model reveals latent components in the multivariate relationship: The increasing importance of a single latent dimension supports the claim that the public exhibits greater ideological constraint than it once did.