A COMPARATIVE STUDY OF BAYESIAN AND MAXIMUM LIKELIHOOD APPROACHES FOR ARCH MODELS WITH EVIDENCE FROM BRAZILIAN FINANCIAL SERIES

The purpose of this study is to address the inference problem of the parameters of autoregressive conditional heteroscedasticity (ARCH) models. Specifically, we present a comparison of the two approaches — Bayesian and Maximum Likelihood (ML) for ARCH models, and the specific mathematical and algorithmic formulations of these approaches. In the ML, estimation we obtain confidence intervals by using the Bootstrap simulation technique. In the Bayesian estimation, we present a reparametrization of the model which allows us to apply prior normal densities to the transformed parameters. The posterior estimates are obtained using Monte Carlo Markov Chain (MCMC) methods. The methodology is exemplified by considering two Brazilian financial time series: the Bovespa Stock Index — IBovespa and the Telebrás series. The order of each ARCH model is selected by using the Bayesian Information Criterion (BIC).