On Loss Functions and Ranking Forecasting Performances of Multivariate Volatility Models
Bibliographic record
Abstract
A large number of parameterizations have been proposed to model conditional variance dynamics in a multivariate framework. However, little is known about the ranking of multivariate volatility models in terms of their forecasting ability. The ranking of multivariate volatility models is inherently problematic because it requires the use of a proxy for the unobservable volatility matrix and this substitution may severely affect the ranking. We address this issue by investigating the properties of the ranking with respect to alternative statistical loss functions used to evaluate model performances. We provide conditions on the functional form of the loss function that ensure the proxy-based ranking to be consistent for the true one – i.e., the ranking that would be obtained if the true variance matrix was observable. We identify a large set of loss functions that yield a consistent ranking. In a simulation study, we sample data from a continuous time multivariate diffusion process and compare the ordering delivered by both consistent and inconsistent loss functions. We further discuss the sensitivity of the ranking to the quality of the proxy and the degree of similarity between models. An application to three foreign exchange rates, where we compare the forecasting performance of 16 multivariate GARCH specifications, is provided.
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How this classification was reachedexpand
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 | 0.003 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.000 |
| Bibliometrics | 0.001 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.001 |
| Research integrity | 0.000 | 0.002 |
| 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 itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, 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".