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

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.