Multivariate volatility modeling is an important tool to estimate the changing volatility as well as correlation in financial time series. Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and Stochastic Volatility (SV) are two representative models in finance and econometrics literature. Recently, multivariate GARCH models with time-varying correlations models have been popularized mainly because of their capabilities in capturing the dynamic structure of volatility and correlation....[ Read more ]

Multivariate volatility modeling is an important tool to estimate the changing volatility as well as correlation in financial time series. Generalized Autoregressive Conditional Heteroscedasticity (GARCH) and Stochastic Volatility (SV) are two representative models in finance and econometrics literature. Recently, multivariate GARCH models with time-varying correlations models have been popularized mainly because of their capabilities in capturing the dynamic structure of volatility and correlation.

The thesis presents simplifications and extensions of Multivariate GARCH (MGARCH) models. In multivariate modeling, time series properties of the interdependence in financial assets can be captured. The major concerns in the multivariate modeling are the capability to capture some important features such as changing volatility and correlation, and the number of parameters to be estimated. Engle (2002) and Tse and Tsui (2002) proposed MGARCH models with dynamic correlations with parsimonious structure. Nonetheless, the number of parameters in both models grows in the power of the number of assets. Two approaches in simplifying the varying conditional correlation MGARCH model are suggested such that the number of parameter increases linearly with the number of assets. Using the two simplifications, it can be more applicable in high dimensional financial data.

In addition, this thesis discusses two extensions of MGARCH model with time-varying conditional correlations. The first extension considers a threshold MGARCH model to capture the mean, volatility and correlations asymmetries in return series. Threshold nonlinearity is incorporated into the mean, volatility and correlation specifications of the MGARCH model.

As the original formulation restricts all dynamic correlations to have the same dynamic structure, the second extension of MGARCH model is to explore a cluster pattern such that similar correlations or financial returns can be grouped into clusters for better understanding the interdependence of different returns while maintaining the parsimony of the original dynamic formulations. Finally, Bayesian methods are adopted for parameters estimation and model comparison in this thesis.