Multivariate GARCH Models with Correlation Clustering

This paper proposes a new clustered correlation multivariate GARCH model (CCMGARCH) that allows conditional correlations to form clusters. This model can generalize the time-varying correlation structure in Tse and Tsui (2002) by determining a natural grouping of the correlations among the series. To estimate the proposed model, we adopt Markov Chain Monte Carlo methods. Two efficient sampling schemes for drawing discrete indicators are also developed. Simulations show that these efficient sampling schemes can save substantial computation time in Monte Carlo procedures involving discrete indicators. In the applications using stock market and exchange rate data, twocluster and three-cluster models are selected using posterior probabilities, implying that the conditional correlation equation should be governed by more than one set of decaying parameters.