Modeling and Estimating GARCH-X and Realized GARCH Using ARWM and GRG Methods

This study evaluates the fitting performance of GARCH-X(1,1) and RealGARCH(1,1) models, which are extensions of GARCH(1,1) model by adding the Realized Kernel measure as an exogenous component, on real data, namely the Financial Times Stock Exchange 100 and Hang Seng stock indices over the period from January 2000 to December 2017. The models assume that the return error follows Normal and Student- t distributions. The parameters of models are estimated by using the Adaptive Random Walk Metropolis (ARWM) method implemented in Matlab and the Generalized Reduced Gradient (GRG) method. The comparison of estimation results shows that the GRG method has a good ability to estimate the models because it provides the estimation results that are close to the results of the ARWM method in terms of relative error. On the basis of Akaike Information Criterion, the RealGARCH models perform better than the GARCH-X models, where the RealGARCH model with Student- t distribution provides the best fit.