Bayesian IGARCH Modeling of Jakarta Composite Index Volatility Using Hamiltonian Monte Carlo Algorithm
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Abstract
Time series models that model volatility in financial data, especially in stock market indices such as the Jakarta Composite Index (JCI), are Generalized Autoregressive Conditional Heteroskedasticity (GARCH) models. Following the ratification of the revised Armed Forces Law in March 2025, the JCI experienced increasing volatility, indicating persistent volatility. The problems in the JCI data require a time series model that can capture persistent volatility, namely the Integrated Generalized Autoregressive Conditional Heteroskedasticity (IGARCH) model. Parameter estimation for IGARCH models generally uses the Maximum Likelihood Estimation (MLE) method, which has limitations in handling parameter uncertainty. The Bayesian approach can address parameter uncertainty through the Markov Chain Monte Carlo (MCMC) methods. Among these, Hamiltonian Monte Carlo (HMC) is more efficient than Metropolis-Hastings and Gibbs Sampling, particularly in exploring complex posterior distributions. This study utilizes daily closing price data of the Jakarta Composite Index (JCI) as the main observation variable, observed from April 3, 2023, to April 9, 2025. This study aims to construct a volatility model for the Jakarta Composite Index (JCI) using a Bayesian IGARCH model with an HMC algorithm. This research only uses the IGARCH(1,1) model. The model has a strong ability to capture the JCI’s volatility structure, and its point forecasts are stable. However, credible intervals reveal the uncertainty level, so the volatility of JCI may decrease or increase.
References
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Chancharat, S. and N. Chancharat (2024). Asymmetric Spillover and Quantile Linkage Between the United States and ASEAN+6 Stock Returns Under Uncertainty. Journal of Open Innovation: Technology, Market, and Complexity, 10(3); 100317
Chaudhary, R., P. Bakhshi, and H. Gupta (2020). Volatility in International Stock Markets: An Empirical Study During COVID-19. Journal of Risk and FinancialManagement, 13(9); 208
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Cryer, J. D. and K.-S. Chan (2008). Time Series Analysis: With Applications in R. Springer, 2 edition
Dolmeta, P., R. Argiento, and S. Montagna (2023). Bayesian GARCH Modeling of Functional Sports Data. Statistical Methods and Applications, 32(2); 401–403
Duane, S., A. D. Kennedy, B. J. Pendleton, and D. Roweth (1987). Hybrid Monte Carlo. Physics Letters B, 195(2); 216–222
Enders,W. (2014). Applied Econometric Time Series. Wiley, 4 edition
Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity With Estimates of the Variance of United Kingdom Inflation. Econometrica; 987–1007
Engle, R. F. and T. Bollerslev (1986). Modelling the Persistence of Conditional Variances. Econometric Reviews, 5(1); 1–50
Fakhriyana, D., Irhamah, and K. Fithriasari (2019). Modeling Jakarta Composite Index with Long Memory and Asymmetric Volatility Approach. In AIP Conference Proceedings, volume 2194. AIP Publishing LLC, page 020025
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Francq, C. and J. Zakoian (2019). GARCH Models: Structure, Statistical Inference and Financial Applications. JohnWiley & Sons
Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin (2019). Bayesian Data Analysis. CRC Press, 3 edition
Girolami, M. and B. Calderhead (2011). Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(2); 123–214
Goldman, J., C. Alexander, and A. Samitas (2023). Uncertainty in Systemic Risks Rankings: Bayesian and Hamiltonian Monte Carlo Methods. Journal of Financial Stability, 69; 104028
González-Pla, F. and L. Lovreta (2022). Modeling and Forecasting Firm-Specific Volatility: The Role of Asymmetry and Long-Memory. Finance Research Letters, 48; 102931
Greene,W. (2018). Econometric Analysis 8th Edition. Pearson Education Limited
Gunawan, I., M. Firdaus, H. Siregar, and M. E. Siregar (2022). Volatility and Stability of ESG Equity in Indonesia Toward Internal and External Shocks. International Journal of Islamic Economics and Finance, 5(2); 335–350
Han, H. and J. Y. Park (2014). GARCHWith Omitted Persistent Covariate. Economics Letters, 124(2); 248–254
Hanada, M. S., Masanori and (2022). MCMC from Scratch : A Practical Introduction to Markov Chain Monte Carlo. Springer
Hanke, J. E. and D.W.Wichern (2014). Business Forecasting. Pearson, new international edition edition
Hendriks, J., A.Wills, B. Ninness, and J. Dahlin (2020). Practical Bayesian System IdentificationUsing HamiltonianMonte Carlo. arXiv preprint arXiv:2011.04117
Hsieh,W.W. (2023). Probability Distributions. In Introduction to Environmental Data Science. Cambridge University Press, pages 65–100
Hyndman, R. J. and G. Athanasopoulos (2018). Forecasting: Principles and Practice. OTexts
Karmakar, S. and D. Roy (2020). BayesianModelling of Time-Varying Conditional Heteroscedasticity. arXiv
Kim, J., D. H. Kim, and H. Jung (2021). Estimating Yield Spreads Volatility Using GARCH-Type Models. The North American Journal of Economics and Finance, 57; 101396
Kusdarwati, H., U. Effendi, and S. Handoyo (2022). Univariate Linear Time Series Analysis: Theory and Its Applications Using RStudio. Universitas Brawijaya Press
Li, Y. (2023). Empirical Analysis of Constructing GARCH Model to Predict Stock Prices With Trading Volume. In Proceedings of the 8th International Conference on Financial Innovation and Economic Development (ICFIED 2023). pages 589–602
Liang, R., B. Qin, and Q. Xia (2024). Bayesian Inference for Mixed Gaussian GARCH-Type Model by Hamiltonian Monte Carlo Algorithm. Computational Economics, 63(1); 193–220
Lim, K. H., N. A. Rahman, and D. Suryanto (2025). Volatility Spillover Between Stock Returns and Oil Prices in ASEAN Countries. International Journal of Energy Economics and Policy, 15(10); 88–100
Maneejuk, P.,W. Huang, andW. Yamaka (2025). Asymmetric Volatility Spillover Effects From Energy, Agriculture, Green Bond, and Financial Market Uncertainty on Carbon Market During Major Market Crisis. Energy Economics; 108430
Mills, T. C. and R. N. Markellos (2008). The Econometric Modelling of Financial Time Series. Cambridge University Press
Montero, J. M., V. Naimy, N. A. Farraj, and R. El Khoury (2024). Natural Disasters, Stock Price Volatility in the Property-Liability Insurance Market and Sustainability: An Unexplored Link. Socio-Economic Planning Sciences, 91; 101791
Nawatmi, S., A. B. Santosa, A. Maskur, and B. Sudiyatno (2023). Predictive VolatilityModels on JKSE and Five Stock Index from Developed Countries. International Journal of Economics, Business and Accounting Research, 7(1); 129–141
Neal, R. M. (2011). MCMC Using Hamiltonian Dynamics. In S. Brooks, A. Gelman, G. Jones, and X. L. Meng, editors, Handbook of Markov Chain Monte Carlo. Chapman and Hall/CRC, pages 113–162
Paixão, R. S. and R. S. Ehlers (2017). Zero Variance and Hamiltonian Monte Carlo Methods in GARCH Models. ArXiv Preprint ArXiv:1710.07693
Perez-Roa, R., S. Infante, G. Barragan, and R. Manzanilla (2024). Bayesian Inference Based on Algorithms: MH, HMC, Mala and Lip-Mala for Prestack Seismic Inversion. EGUSphere, 2024; 1–27
Pollard, J. (2025). Investors Not Happy as Indonesia Eases Limits in Military Law. Asia Financial, December 21
Ponziani, R. (2022). Modeling the Returns Volatility of Indonesian Stock Indices: The Case of SRI-KEHATI and LQ45. Jurnal Ekonomi Modernisasi, 18; 13–21
Rachman, F., A. Nugroho, and B. Prasetyo (2025). Volatility Spillover Effect of Macroeconomic Indicators on Indonesia’s Financial Market. Journal of Public Policy and Management (Bappenas Journal), 6(2); 233–250
Ritter, C. and M. A. Tanner (1992). Facilitating the Gibbs Sampler: The Gibbs Stopper and the Griddy-Gibbs Sampler. Journal of the American Statistical Association, 87(419); 861–868
Setiahutami, S. A. and D. A. Chalid (2024). Volatility Spillovers of Crude Palm Oil, Crude Oil, Coal, Exchange Rates and Indonesian Stock Market (2013–2023). Eduvest: Journal of Universal Studies, 4(5); 3847–3869
Silva, A., L. Pereira, and M. Oliveira (2025). Volatility Spillover and Risk Measurement of Southeast Asian Financial Markets. Brazilian Administration Review (BAR), 22(1); 1–20
Tsay, R. S. (2010). Analysis of Financial Time Series. Wiley, 3rd edition
Wackerly, D. D. (2014). Mathematical Statistics with Applications. Thomson Brooks/Cole
Wei, S. (2006). Time Series Analysis: Univariate andMultivariate Methods. Pearson, Boston, 2nd edition
Xia, Q., H. Wong, J. Liu, and R. Liang (2017). Bayesian Analysis of Power-Transformed and Threshold GARCH Models: A Griddy-Gibbs Sampler Approach. Computational Economics, 50; 353–372
Xie, H., D. Li, and L. Xiong (2016). Exploring the Regional Variance Using ARMA-GARCH Models. Water Resources Management, 30(10); 3507–3518
Yamada, T., K. Ohno, and Y. Ohta (2022). Comparison between the Hamiltonian Monte Carlo Method and the Metropolis–Hastings Method for Coseismic Fault Model Estimation. Earth, Planets and Space, 74(1); 86
Zhao, P., H. Zhu,W. S. H. Ng, and D. L. Lee (2024). From GARCH to Neural Network for Volatility Forecast. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38. pages 16998–17006
Ardia, D. (2008). Financial Risk Management with Bayesian Estimation of GARCH Models: Theory and Applications. Springer
Azimova, T. (2022). Modelling Volatility Transmission in Regional Asian Stock Markets. The Journal of Economic Asymmetries, 26; e00274
Bahtiar, M. R. (2020). Volatility Forecasts Jakarta Composite Index (JCI) and Index Stock Volatility Sector with Estimated Time Series. Indonesian Capital Market Review, 12(1); 2
Bentes, S. R. (2021). How COVID-19 Has Affected Stock Market Persistence? Evidence From the G7’s. Physica A: Statistical Mechanics and Its Applications, 581; 126210
Betancourt, M. (2017). A Conceptual Introduction to Hamiltonian Monte Carlo. arXiv Preprint arXiv:1701.02434
Bollerslev, T. (1986). Generalized Autoregressive Conditional Heteroskedasticity. Journal of Econometrics, 31(3); 307–327
Box, G. E. P., G. M. Jenkins, G. C. Reinsel, and G. M. Ljung (2015). Time Series Analysis: Forecasting and Control. John Wiley & Sons, 5 edition
Brooks, C. (2014). Introductory Econometrics for Finance. Cambridge University Press
Burda, M. and L. Bélisle (2019). CopulaMultivariate GARCH ModelWith Constrained Hamiltonian Monte Carlo. Dependence Modeling, 7(1); 133–149
Chancharat, S. and N. Chancharat (2024). Asymmetric Spillover and Quantile Linkage Between the United States and ASEAN+6 Stock Returns Under Uncertainty. Journal of Open Innovation: Technology, Market, and Complexity, 10(3); 100317
Chaudhary, R., P. Bakhshi, and H. Gupta (2020). Volatility in International Stock Markets: An Empirical Study During COVID-19. Journal of Risk and FinancialManagement, 13(9); 208
Chen, C. W. S., T. Watanabe, and E. M. H. Lin (2023). Bayesian Estimation of Realized GARCH-Type Models With Application to Financial Tail Risk Management. Econometrics and Statistics, 28; 30–46
Cryer, J. D. and K.-S. Chan (2008). Time Series Analysis: With Applications in R. Springer, 2 edition
Dolmeta, P., R. Argiento, and S. Montagna (2023). Bayesian GARCH Modeling of Functional Sports Data. Statistical Methods and Applications, 32(2); 401–403
Duane, S., A. D. Kennedy, B. J. Pendleton, and D. Roweth (1987). Hybrid Monte Carlo. Physics Letters B, 195(2); 216–222
Enders,W. (2014). Applied Econometric Time Series. Wiley, 4 edition
Engle, R. F. (1982). Autoregressive Conditional Heteroscedasticity With Estimates of the Variance of United Kingdom Inflation. Econometrica; 987–1007
Engle, R. F. and T. Bollerslev (1986). Modelling the Persistence of Conditional Variances. Econometric Reviews, 5(1); 1–50
Fakhriyana, D., Irhamah, and K. Fithriasari (2019). Modeling Jakarta Composite Index with Long Memory and Asymmetric Volatility Approach. In AIP Conference Proceedings, volume 2194. AIP Publishing LLC, page 020025
Floros, C. (2008). Modelling Volatility Using GARCHModels: Evidence From Egypt and Israel. Middle Eastern Finance and Economics, 2; 31–41
Francq, C. and J. Zakoian (2019). GARCH Models: Structure, Statistical Inference and Financial Applications. JohnWiley & Sons
Gelman, A., J. B. Carlin, H. S. Stern, D. B. Dunson, A. Vehtari, and D. B. Rubin (2019). Bayesian Data Analysis. CRC Press, 3 edition
Girolami, M. and B. Calderhead (2011). Riemann Manifold Langevin and Hamiltonian Monte Carlo Methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology), 73(2); 123–214
Goldman, J., C. Alexander, and A. Samitas (2023). Uncertainty in Systemic Risks Rankings: Bayesian and Hamiltonian Monte Carlo Methods. Journal of Financial Stability, 69; 104028
González-Pla, F. and L. Lovreta (2022). Modeling and Forecasting Firm-Specific Volatility: The Role of Asymmetry and Long-Memory. Finance Research Letters, 48; 102931
Greene,W. (2018). Econometric Analysis 8th Edition. Pearson Education Limited
Gunawan, I., M. Firdaus, H. Siregar, and M. E. Siregar (2022). Volatility and Stability of ESG Equity in Indonesia Toward Internal and External Shocks. International Journal of Islamic Economics and Finance, 5(2); 335–350
Han, H. and J. Y. Park (2014). GARCHWith Omitted Persistent Covariate. Economics Letters, 124(2); 248–254
Hanada, M. S., Masanori and (2022). MCMC from Scratch : A Practical Introduction to Markov Chain Monte Carlo. Springer
Hanke, J. E. and D.W.Wichern (2014). Business Forecasting. Pearson, new international edition edition
Hendriks, J., A.Wills, B. Ninness, and J. Dahlin (2020). Practical Bayesian System IdentificationUsing HamiltonianMonte Carlo. arXiv preprint arXiv:2011.04117
Hsieh,W.W. (2023). Probability Distributions. In Introduction to Environmental Data Science. Cambridge University Press, pages 65–100
Hyndman, R. J. and G. Athanasopoulos (2018). Forecasting: Principles and Practice. OTexts
Karmakar, S. and D. Roy (2020). BayesianModelling of Time-Varying Conditional Heteroscedasticity. arXiv
Kim, J., D. H. Kim, and H. Jung (2021). Estimating Yield Spreads Volatility Using GARCH-Type Models. The North American Journal of Economics and Finance, 57; 101396
Kusdarwati, H., U. Effendi, and S. Handoyo (2022). Univariate Linear Time Series Analysis: Theory and Its Applications Using RStudio. Universitas Brawijaya Press
Li, Y. (2023). Empirical Analysis of Constructing GARCH Model to Predict Stock Prices With Trading Volume. In Proceedings of the 8th International Conference on Financial Innovation and Economic Development (ICFIED 2023). pages 589–602
Liang, R., B. Qin, and Q. Xia (2024). Bayesian Inference for Mixed Gaussian GARCH-Type Model by Hamiltonian Monte Carlo Algorithm. Computational Economics, 63(1); 193–220
Lim, K. H., N. A. Rahman, and D. Suryanto (2025). Volatility Spillover Between Stock Returns and Oil Prices in ASEAN Countries. International Journal of Energy Economics and Policy, 15(10); 88–100
Maneejuk, P.,W. Huang, andW. Yamaka (2025). Asymmetric Volatility Spillover Effects From Energy, Agriculture, Green Bond, and Financial Market Uncertainty on Carbon Market During Major Market Crisis. Energy Economics; 108430
Mills, T. C. and R. N. Markellos (2008). The Econometric Modelling of Financial Time Series. Cambridge University Press
Montero, J. M., V. Naimy, N. A. Farraj, and R. El Khoury (2024). Natural Disasters, Stock Price Volatility in the Property-Liability Insurance Market and Sustainability: An Unexplored Link. Socio-Economic Planning Sciences, 91; 101791
Nawatmi, S., A. B. Santosa, A. Maskur, and B. Sudiyatno (2023). Predictive VolatilityModels on JKSE and Five Stock Index from Developed Countries. International Journal of Economics, Business and Accounting Research, 7(1); 129–141
Neal, R. M. (2011). MCMC Using Hamiltonian Dynamics. In S. Brooks, A. Gelman, G. Jones, and X. L. Meng, editors, Handbook of Markov Chain Monte Carlo. Chapman and Hall/CRC, pages 113–162
Paixão, R. S. and R. S. Ehlers (2017). Zero Variance and Hamiltonian Monte Carlo Methods in GARCH Models. ArXiv Preprint ArXiv:1710.07693
Perez-Roa, R., S. Infante, G. Barragan, and R. Manzanilla (2024). Bayesian Inference Based on Algorithms: MH, HMC, Mala and Lip-Mala for Prestack Seismic Inversion. EGUSphere, 2024; 1–27
Pollard, J. (2025). Investors Not Happy as Indonesia Eases Limits in Military Law. Asia Financial, December 21
Ponziani, R. (2022). Modeling the Returns Volatility of Indonesian Stock Indices: The Case of SRI-KEHATI and LQ45. Jurnal Ekonomi Modernisasi, 18; 13–21
Rachman, F., A. Nugroho, and B. Prasetyo (2025). Volatility Spillover Effect of Macroeconomic Indicators on Indonesia’s Financial Market. Journal of Public Policy and Management (Bappenas Journal), 6(2); 233–250
Ritter, C. and M. A. Tanner (1992). Facilitating the Gibbs Sampler: The Gibbs Stopper and the Griddy-Gibbs Sampler. Journal of the American Statistical Association, 87(419); 861–868
Setiahutami, S. A. and D. A. Chalid (2024). Volatility Spillovers of Crude Palm Oil, Crude Oil, Coal, Exchange Rates and Indonesian Stock Market (2013–2023). Eduvest: Journal of Universal Studies, 4(5); 3847–3869
Silva, A., L. Pereira, and M. Oliveira (2025). Volatility Spillover and Risk Measurement of Southeast Asian Financial Markets. Brazilian Administration Review (BAR), 22(1); 1–20
Tsay, R. S. (2010). Analysis of Financial Time Series. Wiley, 3rd edition
Wackerly, D. D. (2014). Mathematical Statistics with Applications. Thomson Brooks/Cole
Wei, S. (2006). Time Series Analysis: Univariate andMultivariate Methods. Pearson, Boston, 2nd edition
Xia, Q., H. Wong, J. Liu, and R. Liang (2017). Bayesian Analysis of Power-Transformed and Threshold GARCH Models: A Griddy-Gibbs Sampler Approach. Computational Economics, 50; 353–372
Xie, H., D. Li, and L. Xiong (2016). Exploring the Regional Variance Using ARMA-GARCH Models. Water Resources Management, 30(10); 3507–3518
Yamada, T., K. Ohno, and Y. Ohta (2022). Comparison between the Hamiltonian Monte Carlo Method and the Metropolis–Hastings Method for Coseismic Fault Model Estimation. Earth, Planets and Space, 74(1); 86
Zhao, P., H. Zhu,W. S. H. Ng, and D. L. Lee (2024). From GARCH to Neural Network for Volatility Forecast. In Proceedings of the AAAI Conference on Artificial Intelligence, volume 38. pages 16998–17006
Authors
Maulana, E. D., Sumarminingsih, E. ., Nurjannah, Astuti, A. B. ., & Astutik, S. . (2026). Bayesian IGARCH Modeling of Jakarta Composite Index Volatility Using Hamiltonian Monte Carlo Algorithm. Science and Technology Indonesia, 11(1), 261–279. https://doi.org/10.26554/sti.2026.11.1.261-279
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