MULTIVARIATE VOLATILITY MODELS: AN APPLICATION TO IBOVESPA AND DOW JONES INDUSTRIAL

In this paper, we present a brief description of multivariate GARCH 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 another inference approach to get estimates for the parameters of the models, since we can have great difficulties to obtain 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 as the Markov Chain Monte Carlo (MCMC) methods. As an application to illustrate the proposed methodology, we analyze log-returns of IBOVESPA and Dow Jones Industrial in a weekly basis from 04/27/1993 to 11/03/2008. En este artículo se presenta una breve descripción de modelos GARCH multivariados y se realizan inferencias de la volatilidad de series de tiempo usando un enfoque Bayesiano, utilizando algoritmos de simulación de Monte Carlo (MCMC). Como una aplicación para ilustrar la metodología propuesta, se analizan los logretornos de IBOVESPA y Dow Jones Industrial en una base semanal de 04/27/1993 para 11/03/2008. Dans cet article on présente une brève description des modèles GARCH multivariés et on fait d'analyse d'inférence sur la volatilité des séries temporelles en utilisant une approche bayésienne et des algorithmes de simulation de Monte Carlo (MCMC). Comme application pour illustrer la méthodologie proposée, on étudie des log-rendements d'IBOVESPA et du Dow Jones Industriel sur une base hebdomadaire entre 27/04/1993 et 03/11/2008.