ITSITS

(IJCSAM) International Journal of Computing Science and Applied Mathematics(IJCSAM) International Journal of Computing Science and Applied Mathematics

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 models 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 Excels Solver have similar values to the estimates obtained using MCMC, concluding that Excels Solver has a good ability in estimating the models parameters. Based on AIC values, this study concludes that the NAGARCH(1,1) model under Student-t distribution performs the best.

The study evaluated the performance of asymmetric GARCH models on USD/IDR exchange rate data from 2010 to 2017.The results indicated that Excels Solver is a viable estimation method, comparable to MCMC.Ultimately, the NAGARCH(1,1) model with a Student-t distribution demonstrated the best fit for capturing the volatility characteristics of the data.

Future research could explore the application of these GARCH models to other financial time series data, such as stock prices or commodity futures, to assess their generalizability. Furthermore, investigating the inclusion of exogenous variables, like macroeconomic indicators or global market events, into the GARCH framework could enhance the models predictive power and provide a more comprehensive understanding of volatility dynamics. Finally, a comparative analysis of different MCMC algorithms and optimization techniques beyond those used in this study could lead to more efficient and accurate parameter estimation for these complex models, potentially revealing subtle differences in their performance and robustness.

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