Functional‐coefficient regression models with GARCH errors
Bibliographic record
Abstract
Abstract The GARCH models are widely used to model various financial data with nonlinearity and heteroscedasticity structures. In this article, we propose a functional‐coefficient regression model with GARCH( r , s ) errors to model these kinds of data. To deal with the effect of heteroscedasticity, we introduce a two‐step approach to estimating the unknown coefficient functions and the volatility, which results in unweighted and weighted local linear estimators. Asymptotic properties of the proposed estimators are established. Our results demonstrate that the weighted estimator is more efficient than the unweighted one, and the functional coefficients can be estimated by the weighted estimator as if the volatility was known. Both simulations and real data examples support our theoretical results. In particular, when there are GARCH effects, our two‐step estimator mimics the oracle estimator, with the true volatility being known in advance.
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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".