Three Essays in Bayesian Financial Econometrics

This thesis consists of three chapters in Bayesian financial econometrics. The first chapter proposes new dynamic component models of returns and realized covariance (RCOV) matrices based on time-varying Wishart distributions. Bayesian estimation and model comparison is conducted with a range of multivariate GARCH models and existing RCOV models from the literature. The main method of model comparison consists of a term-structure of density forecasts of returns for multiple forecast horizons. The new joint return-RCOV models provide superior density forecasts for returns from forecast horizons of 1 day to 3 months ahead as well as improved point forecasts for realized covariances. Global minimum variance portfolio selection is improved for forecast horizons up to 3 weeks out. The second chapter proposes a full Bayesian nonparametric procedure to investigate the predictive power of exchange rates on commodity prices for 3 commodity-exporting countries: Canada, Australia and New Zealand. I examine the predictive effect of exchange rates on the entire distribution of commodity prices and how this effect changes over time. A time-dependent infinite mixture of normal linear regression model is proposed for the conditional distribution of the commodity price index. The mixing weights of the mixture follow a Probit stick-breaking prior and are hence time-varying. As a result, I allow the conditional distribution of the commodity price index given exchange rates to change over time nonparametrically. The empirical study shows some new results on the predictive power of exchange rates on commodity prices. The third chapter proposes a flexible way of modeling heterogeneous breakdowns in the volatility dynamics of multivariate financial time series within the framework of MGARCH models. During periods of normal market activities, volatility dynamics are modeled by a MGARCH specification. I refer to any significant temporary deviation of the conditional covariance matrix from its implied GARCH dynamics as a covariance breakdown, which is captured through a stochastic component that allows for changes in the whole conditional covariance matrix. Bayesian inference is used and I propose an efficient posterior sampling procedure. Empirical studies show the model can capture complex and erratic temporary structural change in the volatility dynamics.