Volatility plays an important role in the field of financial econometrics as one of the risk indicators. Many various models address the problem of modeling the volatilities of financial asset returns. This study provides a new empirical performance comparison of the four different GARCH-type models, namely GARCH, GARCH-M, GJR-GARCH, and log-GARCH models based on simulated data and real data such as the DJIA, S&P 500, and S&P CNX Nifty indices on a daily period from January 2000 to December 2017. We also investigate the estimation results obtained using Solver’Excel and verify those results against the results obtained using a Markov chain Monte Carlo method. The simulation study showed that the GARCH model is outperformed by other models. Meanwhile, the empirical study provides evidence that the GJR-GARCH model provides the best fitting, followed by the GARCH-M, GARCH, and log-GARCH models. Furthermore, this study recommends the use of Excel’s Solver in practice when the parameter estimates for GARCH-type model do not close to zero.
Numerous variants of the basic Generalized Autoregressive Conditional Heteroscedasticity (GARCH) models have been proposed to provide good volatility estimating and forecasting. Most of the study does not work Excel’s Solver to estimate GARCH-type models. The first purpose of this study is to provide the capability analyze of the GRG non-linear method built in Excel’s Solver to estimate the GARCH models in comparison to the adaptive random walk Metropolis method in Matlab by own codes. The second contribution of this study is to evaluate some characteristics and performance of the GARCH-M(1,1), GJR(1,1), and log-GARCH(1,1) models with Normal and Student-t error distributions that fitted to financial data. Empirical analyze is based on the application of models and methods to the DJIA, S&P500, and S&P CNX Nifty stock indices. The first empirical result showed that Excel’s Solver’s Generalized Reduced Gradient (GRG) non-linear method has capability to estimate the econometric models. Second, the GJR(1,1) models provide the best fitting, followed by the GARCH-M(1,1), GARCH(1,1), and log-GARCH(1,1) models. This study concludes that Excel’s Solver’s GRG non-linear can be recommended to the practitioners that do not have enough knowledge in the programming language in order to estimate the econometrics models. It also suggests to incorporate a risk premium in the return equation and an asymmetric effect in the variance equation.
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