Modeling and Forecasting Volatility through EGARCH-X and EGARCH-CJ Models

Nugroho, Didit Budi (Universitas Kristen Satya Wacana, Indonesia)
Putri, Benita Dwitya (Universitas Kristen Satya Wacana, Indonesia)
Susanto, Bambang (Universitas Kristen Satya Wacana, Indonesia)

Zero : Jurnal Sains, Matematika, dan Terapan
Vol 9, No 3 (2025): Zero: Jurnal Sains Matematika dan Terapan

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.