Comparison of Mcmc Methods for Estimating Garch Models*

Autoregressive conditional heteroskedasticity (ARCH) models pioneered by Engle (1982) and their extended version have been proven to be very successful in modeling the volatility of financial time series; see Bollerslev et al. (1994). Bayesian inference on ARCH models has been implemented using the importance sampling technique proposed by Geweke (1989) and more recently using Markov chain Monte Carlo (MCMC) methods including Bauwens and Lubrano (1998), Kim et al. (1998), Nakatsuma (2000), Vrontos et al. (2000) and Mitsui and Watanabe (2003). For each integer t, let εt be a model’s prediction error and σ 2 t the variance of εt given information at time t − 1. The most useful ARCH parameterization is the generalized ARCH (GARCH) model introduced by Bollerslev (1986, 1987). The GARCH(p, q) model is given by