Deep Learning and Transformer Architectures for Volatility Forecasting: Evidence from U.S. Equity Indices
Why this work is in the frame
A frame that forgets how it found something cannot be audited. These are the routes that admitted this work.
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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Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.008 | 0.015 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 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 it