Time Series Chaos Detection and Assessment via Scale Dependent Lyapunov Exponent
Bibliographic record
Abstract
Many dynamical systems in a wide range of disciplines -- such as engineering, economy and biology -- exhibit complex behaviors generated by nonlinear components which might result in deterministic chaos. While in lab--controlled setups its detection and level estimation is in general a doable task, usually the same does not hold for many practical applications. This is because experimental conditions imply facts like low signal--to--noise ratios, small sample sizes and not--repeatability of the experiment, so that the performances of the tools commonly employed for chaos detection can be seriously affected. To tackle this problem, a combined approach based on wavelet and chaos theory is proposed. This is a procedure designed to provide the analyst with qualitative and quantitative information, hopefully conducive to a better understanding of the dynamical system the time series under investigation is generated from. The chaos detector considered is the well known Lyapunov Exponent. A real life application, using the Italian Electric Market price index, is employed to corroborate the validity of the proposed approach.
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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".