Bayesian MCMC Approach to the Multicomponent Volatility Jump-augmented Models

GARCH-MIDAS model of Engle et al. (2013) describes the volatility of daily returns as the product of a short-term volatility component, modelled by a Unit GARCH(1,1), and long-term component volatility which is modelled by a macroeconomic variable(s) which are observed at a lower frequency. This model has been applied extensively in volatility modelling using the Maximum Likelihood Estimation (MLE) Method despite that little is known about its finite sample properties. In this thesis, we fill this gap and extend it to other models such as EGARCH-MIDAS, and stochastic volatility models such as SVL-MIDAS and Heston-MIDAS models and their jump augmented versions to capture the leverage effect and the impact of rare events. Results of our first contribution indicate that in-sample and out-sample performance of GARCH type MIDAS models depend on the specification gt whereas τˆt is not sensitive to the choice of the short-term component of the volatility; our simulation and empirical studies suggest that whenever EGARCH(1,1), say, outperforms GARCH(1,1), EGARCH-MIDAS outperforms GARCH-MIDAS; and MLE estimate of GARCH-MIDAS, and EGARCH-MIDAS are not consistent when the returns series contain spikes or its volatility is highly persistent. These results led us to our second main contribution of estimating their parameters and those of their Jump augmented versions using Bayesian approach by overcoming the complexity of their posterior distributions by applying Metropolis Hasting simulation method. Our simulation and empirical studies indicate that our MCMC algorithms successfully capture the jump component and produce accurate estimates when MLE fails. Based on the findings of our first two contributions and the recognized out-performance of stochastic volatility models over GARCH type models, we developed SV-MIDAS, SVL-MIDAS, and Heston-MIDAS with their jump augmented extensions. Our MCMC algorithms can be extended to more complex multi-component volatility models to be considered in our future work.