  We perform the Bayesian inference of a GARCH model by the Metropolis-Hastings
algorithm with an adaptive proposal density. The adaptive proposal density is
assumed to be the Student's t-distribution and the distribution parameters are
evaluated by using the data sampled during the simulation. We apply the method
for the QGARCH model which is one of asymmetric GARCH models and make empirical
studies for for Nikkei 225, DAX and Hang indexes. We find that autocorrelation
times from our method are very small, thus the method is very efficient for
generating uncorrelated Monte Carlo data. The results from the QGARCH model
show that all the three indexes show the leverage effect, i.e. the volatility
is high after negative observations.
