Bayesian Latent Threshold Modeling: Multivariate Time Series and Dynamic Networks

We discuss dynamic network modeling for multivariate time series, exploiting dynamic variable selection and model structure uncertainty strategies based on the recently introduced concept of “latent thresholding.” This dynamic modeling concept addresses a critical and challenging problem in multivariate time series and dynamic modeling: that of inducing formal probabilistic structures that are able to dynamically adapt to temporal changes in the practical relevance/existence of relationships among variables, overlaying the more traditional needs for adapting to and estimating time variation in strengths of relationships when they exist. Bayesian methodology based on dynamic latent thresholding has shown its utility in initial studies in dynamic regression, econometric and financial factor models. From this basis, the current paper involves focused development of dynamic latent thresholding for time-varying, vector autoregressive (TV-VAR) models in increasingly high-dimensions, with the theme of inference on dynamics in network structure. We develop latent thresholding models for both time-varying VAR coefficient matrices and innovation precision matrices. This induces novel classes of dynamic processes over directed and undirected associations in multivariate time series, reflecting dynamics of lagged and contemporaneous “network” dependencies. Applied analyses involving foreign currency exchange rate (FX) time series and electroencephalography (EEG) time series in neurophysiology exemplify latent thresholding as a flexible approach to inferring patterns of temporal change in both structure and strength of existing relationships, opening up new methodology for dynamic network evaluation and prediction.