An Empirical Characteristic Function Approach to VaR Under a Mixture-of-Normal Distribution with Time-Varying Volatility
Bibliographic record
Abstract
This paper considers Value at Risk measures constructed under a discrete mixture of normal distribution on the innovations with time-varying volatility, or MN-GARCH, model. We adopt an approach based on the continuous empirical characteristic function to estimate the param eters of the model using several daily foreign exchange rates' return data. This approach has several advantages as a method for estimating the MN-GARCH model. In particular, under certain weighting measures, a closed form objective distance function for estimation is obtained. This reduces the computational burden considerably. In addition, the characteristic function, unlike its likelihood function counterpart, is always uniformly bounded over parameter space due to the Fourier transformation. To evaluate the VaR estimates obtained from alternative specifications, we construct several measures, such as the number of violations, the average size of violations, the sum square of violations and the expected size of violations. Based on these measures, we find that the VaR measures obtained from the MN-GARCH model outperform those obtained from other competing models.
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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 | 0.006 | 0.030 |
| Meta-epidemiology (narrow) | 0.001 | 0.001 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.002 | 0.002 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.002 | 0.005 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.002 | 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".