  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.
