Markov Chain Monte Carlo on Asymmetric GARCH Model Using the Adaptive Construction Scheme

We perform Markov chain Monte Carlo simulations for a Bayesian inference of the GJR-GARCH model which is one of asymmetric GARCH models. The adaptive construction scheme is used for the construction of the proposal density in the Metropolis-Hastings algorithm and the parameters of the proposal density are determined adaptively by using the data sampled by the Markov chain Monte Carlo simulation. We study the performance of the scheme with the artificial GJR-GARCH data. We find that the adaptive construction scheme samples GJR-GARCH parameters effectively and conclude that the Metropolis-Hastings algorithm with the adaptive construction scheme is an efficient method to the Bayesian inference of the GJR-GARCH model.