Evaluating the Fitting Performance of AGARCH(1,1), NGARCH(1,1), and VGARCH(1,1) Models

Abstract

This study compares the performance of the GARCH(1,1), AGARCH(1,1), NAGARCH(1,1), and VGARCH(1,1) models fitted to real data. The observed real data are the exchange rate of USD against IDR in the daily period from January 2010 to December 2017. The return error of each model is assumed to be Normal, Skew Normal (SN), Skew Curved Normal (SCN), and Student-t distributions. The parameters of each model are estimated using the Non-Linear GRG method in the Excel’s Solver and the ARWM method in MCMC scheme implemented in Scilab program. Estimation result using Excel’s Solver have similar values to the estimates obtained using MCMC, concluding that Excel’s Solver has a good ability in estimating the model parameters. On the bases of AIC (Akaike Information Criterion) values, the NAGARCH(1,1) model provides the best fit under each distribution. Moreover, AIC indicates that the Student-t distribution best fits the observed data, followed by SCN, SN, Normal distributions. Therefore, this study concludes that the NAGARCH(1,1) model under Student-t distribution performs the best.