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Keywords:

  • MCMC methods;
  • mixture autoregressive models;
  • Bayesian model selection;
  • stationarity conditions;
  • volatility

Abstract

In this paper, we present a fully Bayesian analysis of a finite mixture of autoregressive components. Neither the number of mixture components nor the autoregressive order of each component have to be fixed, since we treat them as stochastic variables. Parameter estimation and model selection are performed using Markov chain Monte Carlo methods. This analysis allows us to take into account the stationarity conditions on the model parameters, which are often ignored by Bayesian approaches. Finally, the application to return volatility of financial markets will be illustrated. Our model seems to be consistent with some empirical facts concerning volatility such as persistence, clustering effects, nonsymmetrical dependencies. Copyright © 2006 John Wiley & Sons, Ltd.