In this paper, we present a brief description of ARCH, GARCH and EGARCH models. Usually, their parameter estimates are obtained using maximum likelihood methods. Considering new methodological processes to model the volatilities of time series, we need to use other inference approach to get estimates for the parameters of the models, since we can encouter great difficulties in obtaining the maximum likelihood estimates due to the complexity of the likelihood function. In this way, we obtain the inferences for the volatilities of time series under a Bayesian approach, especially using popular simulation algorithms such as the Markov Chain Monte Carlo (MCMC) methods. As an application to illustrate the proposed methodology, we analyze a financial time series of the Gillette Company ranging from January, 1999 to May, 2003.
ARCH; GARCH; EGARCH; Stochastic Volatility Models; Financial Time Series; Bayesian methodology; MCMC methods
