Modelling conditional moments and correlation with the continuous hidden-threshold-skew-normal distribution
Bibliographic record
Abstract
A key issue in modelling conditional densities of returns of financial assets is the time-variation of conditional volatility. The classic econometric approach models volatility of returns with the generalized autoregressive conditional heteroscedasticity (GARCH) models where the conditional mean and the conditional volatility depend only on historical prices. We propose a new family of distributions in which the conditional distribution depends on a latent continuous factor with a continuum of states. The distribution has an interpretation in terms of a mixture distribution with time-varying mixing probabilities. The distribution parameters have economic interpretations in terms of conditional volatilities and correlations of the returns with the hidden continuous state. We show empirically that this distribution outperforms its main competitor, the mixed normal conditional distribution, in terms of capturing the stylized facts known for stock returns, namely, volatility clustering, leverage effect, skewness, kurtosis and regime dependence.
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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 | 0.000 | 0.000 |
| 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 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".