Volatility Modelling of the JSE Top40 Index: Assessing the GAS Framework Against GARCH and Hybrid GARCH–XGBoost
Bibliographic record
Abstract
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.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.004 | 0.004 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.001 | 0.001 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".