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 stand-alone ARMA(3,2)–EGARCH(1,1) model and a hybrid ARMA(3,2)–EGARCH(1,1)–XGBoost framework. The GAS model is estimated on 3515 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 most accurately produced by the Hybrid ARMA(3,2)–EGARCH(1,1)–XGBoost model (RMSE = 0.1386). The full Diebold-Mariano (DM) test confirms that all pairwise differences in predictive accuracy are statistically significant, and the model confidence set (MCS) procedure identifies the Hybrid model as the sole superior model at the 5% significance level, indicating that both ARMA(3,2)–EGARCH(1,1) and GAS–STD are statistically inferior. Simulation experiments illustrate that the tail behaviour of the Student-t distribution is sensitive to the degrees-of-freedom parameter ν. For example, a Student-t distribution with ν=5 exhibits total kurtosis of approximately 7.32, indicating heavier tails compared to the Gaussian distribution. Overall, GAS–STD is a strong density and risk model for the JSE Top40, while the hybrid framework excels in short-term volatility forecasting.