Real Time Estimation of Multivariate Stochastic Volatility Models

This thesis firstly considers a modelling framework for multivariate volatility in financial time series. As most financial returns exhibit heavy tails and skewness, we are considering a model for the returns based on the skew-t distribution, while the volatility is assumed to follow a Wishart autoregressive process. We define a new type of Wishart autoregressive process and highlight some of its properties and some of its advantages. Particle filter based inference for this model is discussed and a novel approach of estimating static parameters is provided. Furthermore, an alternative methodology for estimating higher dimension data is developed. Secondly, inspired from the idea of Ulig's Wishart process, a new Wishart-Newton model is developed. The approach combines conjugate Bayesian inference while the hyper parameters are estimated by a Newton-Raphson method and here an online volatility estimate algorithm is proposed. The two proposed models are compared with the benchmarking GO-GARCH model in both function execution time and cumulative returns of different dimensional datasets.