Data-Based Parametrization for Affine GARCH Models Across Multiple Time Scales—Roughness Implications
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Bibliographic record
Abstract
This paper revisits the topic of time-scale parameterizations of the Heston–Nandi GARCH (1,1) model to create a new, theoretically valid setting compatible with real financial data. We first estimate parameters using three US market indices and six frequencies to let data reveal the correct, data-implied, time-scale parameterizations. We compared the data-implied parametrization to two popular candidates in the literature, demonstrating structurally different continuous-time limits, i.e., the data favor fractional Brownian motion (fBM)—instead of the standard Brownian motion (BM)-based parametrization. We then propose a theoretically flexible time-scale parameterization compatible with this fBM behavior. In this context, a fractional derivative analysis of our empirically based parametrization is performed, confirming an anomalous diffusion in the continuous-time limit. Such a finding is yet another endorsement of the recent and popular stylized fact known as rough volatility.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.001 | 0.004 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.001 |
| Open science | 0.002 | 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