A Hybrid EGARCH–Informer Model with Consistent Risk Calibration for Volatility and CVaR Forecasting

Ming Che Lee ()
Additional contact information
Ming Che Lee: Applied Artificial Intelligence Department, Ming Chuan University, Taoyuan 320, Taiwan

Mathematics, 2025, vol. 13, issue 19, 1-22

Abstract: This study proposes a hybrid EGARCH-Informer framework for forecasting volatility and calibrating tail risk in financial time series. The econometric layer (EGARCH) captures asymmetric and persistent volatility dynamics, while the attention layer (Informer) models long-range temporal dependence with sparse attention. The framework produces horizon-specific forecasts (H = 1 and H = 5) that are mapped to VaR and CVaR at α = 0.95 and 0.99. Evaluation covers pointwise accuracy (MAE, RMSE) and risk coverage calibration (CVaR bias and Kupiec’s unconditional coverage), complemented by Conditional Coverage (CC) and Dynamic Quantile (DQ) diagnostics, and distributional robustness via a Student-t mapping of VaR/CVaR. Across four U.S. equity indices (SPX, IXIC, DJI, SOX), the hybrid matches GARCH at the short horizon and yields systematic error gains at the longer horizon while maintaining higher calibration quality than deep learning baselines. MAE and RMSE values remain near 0.0002 at H = 1, with relative improvements of 2–6% at H = 5. CVaR bias stays tightly bounded; DQ rarely rejects, and CC is stricter but consistent with clustered exceedances, and the Student-t results keep the median hit rates near nominal with small, mildly conservative CVaR biases. These findings confirm the hybrid model’s robustness and transferability across market conditions.

Keywords: volatility forecasting; EGARCH-Informer; tail risk; value-at-risk; conditional value-at-risk; risk calibration (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
References: Add references at CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/13/19/3108/pdf (application/pdf)
https://www.mdpi.com/2227-7390/13/19/3108/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:13:y:2025:i:19:p:3108-:d:1760321

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().