Evaluating the Fitting Performance of AGARCH(1,1), NAGARCH(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 USD exchange rate against IDR in the daily period from January 2010 to December 2017. To identify the superiority and evaluate the performance of those models in capturing the heavy-tailed and skewed character in exchange rate distribution, the return error is assumed to be the Normal, Skew Normal (SN), Skew Curved Normal (SCN), and Student-t distributions. The model's parameters are estimated using the GRG Non-Linear method in Excel Solver and the ARWM method in the MCMC scheme implemented in the Scilab program. Estimation results 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's parameters. Based on AIC values, this study concludes that the NAGARCH(1,1) model under Student-t distribution performs the best.