Bayesian analysis of ARMA–GARCH models: A Markov chain sampling approach

We develop a Markov chain Monte Carlo method for a linear regression model with an ARMA(p, q)-GARCH(r, s) error. To generate a Monte Carlo sample from the joint posterior distribution, we employ a Markov chain sampling with the Metropolis–Hastings algorithm. As illustration, we estimate an ARMA–GARCH model of simulated time series data.