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A Bayesian estimation of a GARCH model is performed for US Dollar/JapaneseYen exchange rate by the Metropolis-Hastings algorithm with a proposal densitygiven by the adaptive construction scheme. In the adaptive construction schemethe proposal density is assumed to take a form of a multivariate Student'st-distribution and its parameters are evaluated by using the sampled data andupdated adaptively during Markov Chain Monte Carlo simulations. We find thatthe autocorrelation times between the data sampled by the adaptive constructionscheme are considerably reduced. We conclude that the adaptive constructionscheme works efficiently for the Bayesian inference of the GARCH model.

Bayesian estimation of GARCH model with an adaptive proposal density