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

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