Bayesian Analysis of Latent Threshold Dynamic Models

Time series modeling faces increasingly high-dimensional problems in many scientific areas. Lack of relevant, data-based constraints typically leads to increased uncer-tainty in estimation and degradation of predictive performance. This dissertation addresses these general questions with a new and broadly applicable idea based on latent threshold models. The latent threshold approach is a model-based framework for inducing data-driven shrinkage of elements of parameter processes, collapsing them fully to zero when redundant or irrelevant while allowing for time-varying non-zero values when supported by the data. This dynamic sparsity modeling technique is implemented in broad classes of multivariate time series models with application tovarious time series data. The analyses demonstrate the utility of the latent threshold idea in reducing estimation uncertainty and improving predictions as well as model interpretation. Chapter 1 overviews the idea of the latent threshold approach and outlines the dissertation. Chapter 2 introduces the new approach to dynamic sparsity using latent threshold modeling and also discusses Bayesian analysis and computation for model fitting. Chapter 3 describes latent threshold multivariate models for a wide range of applications in the real data analysis that follows. Chapter 4 provides US and Japanese macroeconomic data analysis using latent threshold VAR models. Chapter 5 analyzes time series of foreign currency exchange rates (FX) using latent thresh-old dynamic factor models. Chapter 6 provides a study of electroencephalographic (EEG) time series using latent threshold factor process models. Chapter 7 develops a new framework of dynamic network modeling for multivariate time series using the latent threshold approach. Finally, Chapter 8 concludes the dissertation with open questions and future works.