Kim, Shephard, and Chib (1998) provided a Bayesian analysis of stochastic volatility models based on a fast and reliable Markov chain Monte Carlo (MCMC) algorithm. Their method ruled out the leverage effect, which is known to be important in applications. Despite this, their basic method has been extensively used in the financial economics literature and more recently in macroeconometrics. In this paper we show how the basic approach can be extended in a novel way to stochastic volatility models with leverage without altering the essence of the original approach. Several illustrative examples are provided.

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 threshold dynamic factor models. Chapter 6 provides a study of electroencephalographic iv (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.

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