Bayesian Estimation of Generalized Auto Regressive Conditionally Heteroscedastic Model with an Application to Foolad Mobarakeh Stock Returns

Problems in economics and finance have recently motivated the study of the volatility of a time series data setting. Several time series models to concern the volatility of such data have been considered. Although the Auto Regressive Moving Average (ARMA) models assume a constant variance, models such as the Auto Regressive Conditionally Heteroscedastic (ARCH) models are developed to the model changes in volatility. In this paper, we indicate that the generalized ARCH (GARCH) models which have been proposed are useful in many economics and financial studies. We thus develop both probabilistic properties and the Bayesian estimation method of a GARCH (1, 1) model. We then illustrate the model on Foolad Mobarakeh (F.M) daily returns from 2007 to 2012. Further we forecast future values of conditional variance of returns.