Bayesian Applications in Financial Econometrics

This thesis consists of three chapters in Bayesian financial econometrics. The three chapters apply both Bayesian nonparametric and parametric methods to financial market and macroeconomic time series. Chapter 1 extends popular discrete time short-rate models to include Markov switching of infinite dimension. This is a Bayesian nonparametric model that allows for changes in the unknown conditional distribution over time. Applied to weekly U.S. data we find significant parameter change over time and strong evidence of non-Gaussian conditional distributions. Our new model with an hierarchical prior provides significant improvements in density forecasts as well as point forecasts. We find evidence of recurring regimes as well as structural breaks in the empirical application. Chapter 2 studies the joint dynamic behaviour between stock market returns and real economic growth rates. Their relationship is an important empirical question in finance and macroeconomics. This chapter investigates their linkage by proposing a vector autoregressive infinite hidden Markov model. Our model has two advantages over the existing approaches in the literatures. In contrast to Markov switching models with fixed states, our model will learn the number of states from the data rather than fixing it a priori. The vector autoregressive setting in our model allows the joint time series of stock market returns and real growth rates to share the same unobserved state variable. Compared to existing models, our model shows significant improvements in out-of-sample density forecast accuracy. This paper demonstrates the predictive power of stock market returns for future growth rates are better captured by the unobserved states variables, rather than the lagged stock market returns. Chapter 3 studies the predictive power of oil price information for forecasting the U.S. industrial production. Oil price information is divided into two distinct categories: nominal oil price changes and oil price shocks using four definitions proposed in the literature. Previous work has documented lack of predictive relationship of oil price changes but significant predictive power of oil price shocks for U.S. economic growth. However, existing studies focused only on predicting the mean of the economic growth using classical point forecast techniques. As a contribution to the existing literature, we propose a new forecasting model for the analyzed relationship where oil price shocks have the additional flexibility to influence both the mean and the variance of U.S. industrial production. Our forecast is well performed using the Bayesian predictive likelihood as opposed to classical point estimate. We show that the new model for oil price shocks outperforms existing models in terms of forecasting ability. We further confirm previous findings regarding the lack of predictive power of nominal oil price changes.Ph.D