Inference methods in time-varying linear diffusion processes
Bibliographic record
Abstract
In this paper, we introduce a class of inhomogeneous diffusion processes which preserve periodic mean-reverting level and we study the ergodicity of the introduced processes. In particular, the proposed class of processes is suitable for modeling the datasets with a cyclical trend. Such stochastic processes can be used for modeling diverse financial data. We also consider inference problems concerning the drift parameter of the proposed diffusion process. We derive the unrestricted maximum likelihood estimator (UMLE) and the restricted maximum likelihood estimator (RMLE) as well as their joint asymptotic normality. We also construct some shrinkage estimators (SEs) and a test for testing the restriction as well as its asymptotic power. Further, we compare the relative efficiency of the proposed estimators. Finally, the obtained simulation results corroborate our theoretical findings and the applications of the proposed methods are illustrated via an analysis of financial markets.
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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 | 0.001 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.001 |
| 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".