On a dynamic mixture GARCH model

Abstract

This paper proposes a new mixture GARCH model with a dynamic mixture proportion. The mixture Gaussian distribution of the error can vary from time to time. The Bayesian Information Criterion and the EM algorithm are used to estimate the number of parameters as well as the model parameters and their standard errors. The new model is applied to the S&P500 Index and Hang Seng Index and compared with GARCH models with Gaussian error and Student's t error. The result shows that the IGARCH effect in these index returns could be the result of the mixture of one stationary volatility component with another non-stationary volatility component. The VaR based on the new model performs better than traditional GARCH-based VaRs, especially in unstable stock markets. Copyright © 2008 John Wiley & Sons, Ltd.