Deep Learning and Transformer Architectures for Volatility Forecasting: Evidence from U.S. Equity Indices
Bibliographic record
Abstract
Volatility forecasting plays a crucial role in financial markets, portfolio management, and risk control. Classical econometric models such as GARCH, ARIMA, and HAR-RV are widely used but face limitations in capturing the nonlinear and regime-dependent dynamics of financial volatility. This study compares traditional econometric models (HAR-RV, ARIMA, GARCH) with deep learning (DL) architectures (LSTM, CNN-LSTM, PatchTST-lite, and Vanilla Transformer) in forecasting realized variance (RV) for major U.S. equity indices (S&P 500, NASDAQ 100, and the Dow Jones Industrial Average) over the period 2000–2025. RV is used as the dependent variable because it is a standard model-free proxy for market volatility. Forecast accuracy is evaluated across forecast horizons of h = 1, 5, 22 days using QLIKE, RMSE, and MAE, along with Diebold–Mariano (DM) significance tests and overfitting diagnostics. Results show that Transformer-based models achieve the lowest errors and strongest generalization, particularly at short horizons and during volatile periods. Overall, the findings highlight the growing advantage of AI-driven models in delivering stable and economically meaningful volatility forecasts, supporting more effective portfolio allocation and risk management—especially in environments marked by rapid market shifts and structural breaks.
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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 | 0.002 | 0.008 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| Science and technology studies | 0.000 | 0.000 |
| 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".