Volatility Modelling of the JSE Top40 Index: Assessing the GAS Framework Against GARCH and Hybrid GARCH–XGBoost

This paper studies the volatility dynamics of the JSE Top40 Index by estimating a univariate GAS model with time-varying location, scale, and shape parameters (identity score scaling) and comparing its density and point-forecast performance against a standalone ARMA(3,2)-EGARCH(1,1) model and a hybrid ARMA(3,2)-EGARCH(1,1)-XGBoost framework. The GAS model is estimated on 3,515 daily observations, and several conditional densities are examined. The Student-t GAS model (GAS-STD) obtains the lowest information criteria within the GAS family (AIC = 10,188.142; BIC = 10,243.626) and exhibits statistically significant persistence in location and scale dynamics. Statistical diagnostics provide evidence of correct density calibration (Normalised Log Score = 1.1932; Uniform score = 0.4417), although residual skewness remains (IID-Test skewness p=0.0134). Out-of-sample analysis shows that GAS-STD performs strongly in density and risk forecasting, producing accurate 5% VaR and ES paths and passing coverage backtests (Kupiec LRuc p=0.8414; DQ p=0.2281). However, short-horizon point forecasts are best delivered by the hybrid ARMA-EGARCH-XGBoost model (RMSE = 0.1386), with Diebold-Mariano tests confirming a transitive ranking: Hybrid > ARMA-EGARCH > GAS-STD. Simulation experiments highlight the sensitivity of tail behaviour to degrees-of-freedom (e.g., kurtosis ν=5≈7.32). Overall, GAS-STD is a strong density and risk model for the JSE Top40, while the hybrid framework excels in short-term volatility forecasting.