||In this dissertation, we employ the generalized method of moments (GMM) to estimate model parameters in the generalized autoregressive conditional heteroskedastic models. GMM introduced in Hansen (1982) not only provides us a simple way in estimating the parameters in the conditional heteroskedastic models, but also relax the distributional assumption in the maximum likelihood (ML) estimation. Thus, the GMM approach gives a particular useful solution for an important source of specification error. Under some suitable conditions, Hansen (1982) showed that GMM estimator is consistent and asymptotically normal. Simulation results show that GMM estimators have a good performance in estimating the parameters in the GARCH (1,1) regression model. Finally, the GMM is then used to estimate a GARCH model of the HANG SENG INDEX.