Posterior Analysis of the Multiplicative Heteroscedasticity Model

In this paper, we show how to use Bayesian approach in the multiplicative heteroscedasticity model proposed by Harvey (1976), where the Gibbs sampler and the Metropolis-Hastings (MH) algorithm are applied. Some candidate-generating densities are considered in our Metropolis-Hastings algorithm. We carry out Monte Carlo study to examine the properties of the estimates via Bayesian approach and its traditional counterpart, i.e., the modified two-step estimator (M2SE), the maximum likelihood estimator (MLE) and Harvey’s three-step estimator (H3SE). Our results of Monte Carlo study show that candidate-generating densities chosen in our paper are suitable, and Bayesian approach shows better performance than the traditional counterpart in the criterion of the interquartile range and root mean square error. Key word: Multiplicative Heteroscedasticity, Bayesian Approach, the Metropolis-Hastings Algorithm, Sampling Density. ∗Corresponding author ([email protected]).