Modelos estocásticos com heterocedasticidade: Uma abordagem Bayesiana para os retornos do Ibovespa

Abstract

Current research compares the Bayesian estimates obtained for the parameters of processes of ARCH family with normal and Student's t distributions for the conditional distribution of the return series. A non-informative prior distribution was adopted and a reparameterization of models under analysis was taken into account to map parameters' space into real space. The procedure adopts a normal prior distribution for the transformed parameters. The posterior summaries were obtained by Monte Carlo Markov Chain (MCMC) simulation methods. The methodology was evaluated by a series of Bovespa Index returns and the predictive ordinate criterion was employed to select the best adjustment model to the data. Results show that, as a rule, the proposed Bayesian approach provides satisfactory estimates and that the GARCH process with Student's t distribution adjusted better to the data.