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Keywords:

  • clustering;
  • discrete indicator variables;
  • efficient sampling scheme;
  • Markov chain Monte Carlo;
  • multivariate GARCH models;
  • volatility

ABSTRACT

A new clustered correlation multivariate generalized autoregressive conditional heteroskedasticity (CC-MGARCH) model that allows conditional correlations to form clusters is proposed. This model generalizes the time-varying correlation structure of Tse and Tsui (2002, Journal of Business and Economic Statistics 20: 351–361) by classifying the correlations among the series into groups. To estimate the proposed model, Markov chain Monte Carlo methods are adopted. Two efficient sampling schemes for drawing discrete indicators are also developed. Simulations show that these efficient sampling schemes can lead to substantial savings in computation time in Monte Carlo procedures involving discrete indicators. Empirical examples using stock market and exchange rate data are presented in which two-cluster and three-cluster models are selected using posterior probabilities. This implies that the conditional correlation equation is likely to be governed by more than one set of decaying parameters. Copyright © 2011 John Wiley & Sons, Ltd.