Multivariate Volatility Measures and Models with Applications

Abstract

This thesis explores methodologies for modelling and estimating correlation and covariance dynamics, presenting advancements in statistical approaches and their applications across multiple domains. We provide a comprehensive literature review of existing methodologies for modelling covariance matrices, focusing on their advantages, limitations, and practical implications, which highlights the need for efficient estimators and dynamic modelling techniques to address challenges such as heteroskedasticity, non-positive definiteness, and dynamic correlation structures. With our proposed range-based correlation matrix measures, we extend the two-stage multivariate Conditional Autoregressive Range Model (MCARR)-return models to directly model covariance matrix series using the Wishart distribution. Through simulation studies, we compare two approaches: modelling the covariance matrices and modelling the variances and correlation matrices. Correlation matrix modelling demonstrates better performance, guided by specific priors and stationary conditions.