Chief Investment OfficerCharles Schwab Investment Management in San Francisco, California
Latent Structure in Bayesian Multivariate Time Series Models
This dissertation introduces new classes of models and approaches to multivariate time series analysis and forecasting, with a focus on various problems in which time series structure is driven by underlying latent processes of key interest. The identification of latent structure and common features in multiple time series is first studied using wavelet based methods and Bayesian time series decompositions of certain classes of dynamic linear models. The results are applied to turbulence and geochemical time series data, the latter involving development of new time series models for latent time-varying autoregressions with heavy-tailed components for quite radically ill-behaved series. Natural extensions and generalizations of these models lead to novel developments of two key model classes, dynamic factor models for multivariate financial time series with stochastic volatility components, and multivariate dynamic generalized linear models for non-Gaussian longitudinal time series. These two model classes are related through common statistical structure, and the dissertation discusses issues of Bayesian model specification, model fitting and computation for posterior and predictive analysis that are common to the two model classes. Two motivating applications are discussed, one in each of the two model classes. The first concerns short term forecasting and dynamic portfolio allocation, illustrated in a study of the dynamic factor structure of daily spot exchange rates for a selection of international currencies. The second application involves analyses of time series of collections of many related binomial outcomes and arises in a project in health care quality monitoring with the Veterans Affairs (VA) hospital system.