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All Journal BAREKENG: Jurnal Ilmu Matematika dan Terapan Zero : Jurnal Sains, Matematika, dan Terapan
Bambang Susanto
Universitas Kristen Satya Wacana, Indonesia
Agriculture, Biological Sciences & Forestry Chemistry Computer Science & IT Control & Systems Engineering Economics, Econometrics & Finance Energy Engineering Mathematics Mechanical Engineering Physics Transportation

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Modeling and Forecasting Volatility through EGARCH-X and EGARCH-CJ Models Didit Budi Nugroho; Benita Dwitya Putri; Bambang Susanto
ZERO: Jurnal Sains, Matematika dan Terapan Vol 9, No 3 (2025): Zero: Jurnal Sains Matematika dan Terapan
Publisher : UIN Sumatera Utara

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30829/zero.v9i3.26532

Abstract

This study compares the performance of EGARCH-X and EGARCH-CJ models in forecasting financial market volatility using daily TOPIX data (2004-2011). Model parameters were estimated using an efficient Bayesian MCMC framework. The results indicate that the EGARCH-CJ model, which decomposes volatility into continuous and jump components, provides a superior in-sample fit. More importantly, in out-of-sample forecasting, the EGARCH-CJ model demonstrates significantly better accuracy for medium- and long-term horizons (e.g., MSE reductions up to 30% at the 5-day horizon, with significant Diebold-Mariano statistics). In contrast, the standard EGARCH model remains more effective for short-term forecasts. These findings underscore the importance of explicitly modeling jump dynamics for medium-term risk management in the Japanese stock market, offering valuable insights for financial modelers and risk managers.
ENHANCING VOLATILITY MODELING WITH LOG-LINEAR REALIZED GARCH-CJ: EVIDENCE FROM THE TOKYO STOCK PRICE INDEX Didit Budi Nugroho; Zefania Sasongko Putri; Bambang Susanto
BAREKENG: Jurnal Ilmu Matematika dan Terapan Vol 20 No 1 (2026): BAREKENG: Journal of Mathematics and Its Application
Publisher : PATTIMURA UNIVERSITY

Show Abstract | Download Original | Original Source | Check in Google Scholar | DOI: 10.30598/barekengvol20iss1pp0881-0894

Abstract

This study compares the Log-linear Realized GARCH (LRG) and its extension with Continuous and Jump components (LRG-CJ) in modeling the volatility of financial assets, using daily data from the Tokyo Stock Price Index (TOPIX) over 2004–2011. The urgency arises from the need for more accurate volatility models during turbulent periods such as the 2008 Global Financial Crisis and the 2011 Great East Japan Earthquake, where markets exhibit both smooth fluctuations and abrupt jumps. Methodologically, the LRG-CJ framework introduces a novel integration of continuous and jump decomposition into the LRG structure, offering an applied innovation to high-frequency volatility modeling. Realized Volatility (RV) was calculated from 1-, 5-, and 10-minute intraday data and decomposed into continuous and jump components. Parameter estimation employed the Adaptive Random Walk Metropolis (ARWM) within a Markov Chain Monte Carlo algorithm, while model performance was assessed using multiple information criteria and out-of-sample forecast evaluations. The empirical results reveal that incorporating continuous and jump components improves volatility modeling accuracy, forecasting, and Value-at-Risk estimation. However, these benefits are frequency-dependent: the LRG-CJ model shows superior in-sample fit for 1-minute RV but provides the strongest out-of-sample forecasting and risk prediction at lower frequencies (5- and 10-minute intervals). This highlights that while jumps are best identified at ultra-high frequencies, their predictive value is most effectively captured in slightly aggregated data. The originality of this study lies in being the first empirical application of LRG-CJ, demonstrating how continuous–jump decomposition interacts with the dual-equation structure of LRG, which has not been examined in TGARCH or APARCH contexts. Limitations include sensitivity to microstructure noise in very high-frequency data and computational challenges in parameter convergence. Overall, the findings underscore the novelty and practical importance of the LRG-CJ framework for risk management, offering actionable guidance for aligning volatility models with data frequency
Co-Authors Benita Dwitya Putri Didit Budi Nugroho Didit Budi Nugroho Zefania Sasongko Putri