Long-time fluctuations in a dynamical model of stock market indices
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Bibliographic record
Abstract
Financial time series typically exhibit strong fluctuations that cannot be described by a Gaussian distribution. Recent empirical studies of stock market indices examined whether the distribution P(r) of returns r(tau) after some time tau can be described by a (truncated) Lévy-stable distribution L(alpha)(r) with some index 0<alpha< or =2. While the Lévy distribution cannot be expressed in a closed form, one can identify its parameters by testing the dependence of the central peak height on tau as well as the power-law decay of the tails. In an earlier study [R. N. Mantegna and H. E. Stanley, Nature (London) 376, 46 (1995)] it was found that the behavior of the central peak of P(r) for the Standard & Poor 500 index is consistent with the Lévy distribution with alpha=1.4. In a more recent study [P. Gopikrishnan et al., Phys. Rev. E 60, 5305 (1999)] it was found that the tails of P(r) exhibit a power-law decay, with an exponent alpha congruent with 3, thus deviating from the Lévy distribution. In this paper we study the distribution of returns in a generic model that describes the dynamics of stock market indices. For the distributions P(r) generated by this model, we observe that the scaling of the central peak is consistent with a Lévy distribution while the tails exhibit a power-law distribution with an exponent alpha>2, namely, beyond the range of Lévy-stable distributions. Our results are in agreement with both empirical studies and reconcile the apparent disagreement between their results.
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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) | 0.001 | 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) | 0.001 | 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 it