Bayesian Estimation of the GARCH(1,1) Model with Normal Innovations

In this article, we propose the Bayesian estimation of the parsimonious but effective GARCH(1,1) model with Normal innovations. We sample the parameters joint posterior distribution using the approach suggested by Nakatsuma (1998). As a first step, we fit the model to foreign exchange log-returns time series and compare the Maximum Likelihood and the Bayesian estimates. Next, we illustrate some appealing aspects of the Bayesian approach through interesting probabilistic statements made on the parameters.