Copula multivariate GARCH model with constrained Hamiltonian Monte Carlo
Bibliographic record
Abstract
The Copula Multivariate GARCH (CMGARCH) model is based on a dynamic copula function with time-varying parameters. It is particularly suited for modelling dynamic dependence of non-elliptically distributed financial returns series. The model allows for capturing more flexible dependence patterns than a multivariate GARCH model and also generalizes static copula dependence models. Nonetheless, the model is subject to a number of parameter constraints that ensure positivity of variances and covariance stationarity of the modeled stochastic processes. As such, the resulting distribution of parameters of interest is highly irregular, characterized by skewness, asymmetry, and truncation, hindering the applicability and accuracy of asymptotic inference. In this paper, we propose Bayesian analysis of the CMGARCH model based on Constrained Hamiltonian Monte Carlo (CHMC), which has been shown in other contexts to yield efficient inference on complicated constrained dependence structures. In the CMGARCH context, we contrast CHMC with traditional random-walk sampling used in the previous literature and highlight the benefits of CHMC for applied researchers. We estimate the posterior mean, median and Bayesian confidence intervals for the coefficients of tail dependence. The analysis is performed in an application to a recent portfolio of S&P500 financial asset returns.
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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 | 0.001 |
| Meta-epidemiology (broad) | 0.002 | 0.001 |
| Bibliometrics | 0.001 | 0.002 |
| Science and technology studies | 0.001 | 0.001 |
| Scholarly communication | 0.002 | 0.002 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.002 | 0.002 |
| Insufficient payload (model declined to judge) | 0.005 | 0.001 |
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".