We estimate by Bayesian inference the mixed conditional heteroskedasticity model of (Haas, Mittnik, and Paolella 2004a). We construct a Gibbs sampler algorithm to compute posterior and predictive densities. The number of mixture components is selected by the marginal likelihood criterion. We apply the model to the SP500 daily returns.
Bauwens, L., & Rombouts, J. (2005). Bayesian inference for the mixed conditional heteroskedasticity model (ECON Discussion Papers 2005/58). https://hdl.handle.net/2078.5/128661