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Journal : international journal of computing science and applied mathematics-ijcsam

Modeling and Estimating GARCH-X and Realized GARCH Using ARWM and GRG Methods Didit Budi Nugroho; Melina Tito Wijaya; Hanna Arini Parhusip
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 11 No. 1 (2025)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.12962/j24775401.ijcsam.v11i1.4309

Abstract

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.
Evaluating the Fitting Performance of AGARCH(1,1), NAGARCH(1,1), and VGARCH(1,1) Models Didit Budi Nugroho; Veny M. Ningtyas; Hanna A. Parhusip
(IJCSAM) International Journal of Computing Science and Applied Mathematics Vol. 9 No. 2 (2023)
Publisher : LPPM Institut Teknologi Sepuluh Nopember

Show Abstract | Download Original | Original Source | Check in Google Scholar

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.
Co-Authors A.A. Ketut Agung Cahyawan W Adi Setiawan Adi Setiawan Adrianus Herry Heriadi Adrianus Herry Heriadi Alfagustina, Yumita Cristin ALOYSIUS JOAKIM FERNANDEZ Atyanta Nika Rukmasari Bambang Susanto Bambang Susanto Beni Utomo Bernadus Aryo Adhi Wicaksono Carolina Febe Ronicha Putri Denny Indrajaya Denny Indrajaya Didit Budi Nugroho Didit Budi Nugroho Didit Budi Nugroho Djoko Hartanto Djoko Hartanto Eduardus Albert Winarto Endang Warsiki Fachrurrozi Fachrurrozi Fachrurrozi Fachrurrozi Faldy Tita Fetriks Theo Sarita Fika Widya Pratama Fitri, Nirmala Ayu Andika Gede Sutresna Wijaya Goni, Abdiel Wilyar Hariadi, Adrianus Herry Heriadi, Adrianus Herry Hindriyanto Dwi Purnomo Indrajaya, Denny Isman Mulyadi Triatmoko Istiarsi Saptuti Sri Kawuryan Istiarsih Saputri Sri Kawuryan Jane Labadin Jane Labadin Johanes Dian Kurniawan Johanes Dian Kurniawan Johanes Dian Kurniawan Jordi Enal Ambat Karina Bianca Lewerissa Karina Bianca Lewerissa Kristia Anggraeni Kristoko Dwi Hartomo Larasati, Mitchella Sinta Lea, Lea Leopoldus Ricky Sasongko Lilik Linawati Linda Ariany Mahastanti Mauliddha Rachmi Melina Tito Wijaya Mitchella Sinta Larasati Mitha Febby R. Donggori Mitha Febby R. Donggori Nafisah Riskya Hasna Nugroho Dwi Susanto Nugroho, Didit B. Obed Christian Dimitrio Om Prakash Vyas Parung, Ratu Anggriani Tangke Petrus Priyo Santosa Pradani, Wynona Adita Puput Retno Muninggar Purwoko, Agus Puspasari, Magdalena Dwi Rudhito, Andy Santosa, Petrus Priyo Sari, Devina Intan Sri Kawuryan, Istiarsi Saptuti Sri Suryasatriya Trihandaru Susetyo, Yosia Adi Theo Sarita, Fetriks Titilias, Y A Urosidin, Nur I. M. Veny M Ningtyas Veny M. Ningtyas Wijaya, Melina Tito Wijayanti, Yunita Puput Wulandari, Nadya Putri Yohanes Sardjono Yohanes Sardjono Yohanes Sardjono Yohanes Sardjono, Yohanes Yohannes Sardjono Yosia Adi Susetyo Yusuf Kurniawan