Bayesian IGARCH Modeling of Jakarta Composite Index Volatility Using Hamiltonian Monte Carlo Algorithm

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.