Bayesian Analysis of Realized Matrix-Exponential GARCH Models

This study develops a new realized matrix-exponential GARCH (MEGARCH) model, which uses the information of returns and realized measure of co-volatility matrix simultaneously. An alternative multivariate asymmetric function to develop news impact curves is also considered. We consider Bayesian Markov chain Monte Carlo estimation to allow non-normal posterior distributions and illustrate the usefulness of the algorithm with numerical simulations for two assets. We compare the realized MEGARCH models with existing multivariate GARCH class models for three US financial assets. The empirical results indicate that the realized MEGARCH models outperform the other models regarding out-of-sample performance. The news impact curves based on the posterior densities provide reasonable results.