Circular-Statistics-Based Estimators and Tests for the Index Parameter α of Distributions for High-Volatility Financial Markets
Bibliographic record
Abstract
The distributions for highly volatile financial time-series data are playing an increasingly important role in current financial scenarios and signal analyses. An important characteristic of such a probability distribution is its tail behaviour, determined through its tail thickness. This can be achieved by estimating the index parameter of the corresponding distribution. The normal and Cauchy distributions, and, sometimes, a mixture of the normal and Cauchy distributions, are suitable for modelling such financial data. The family of stable distributions can provide better modelling for such financial data sets. Financial data in high-volatility markets may be better modelled, in many cases, by the Linnik distribution in comparison to the stable distribution. This highly flexible family of distributions is better capable of modelling the inflection points and tail behaviour compared to the other existing models. The estimation of the tail thickness of heavy-tailed financial data is important in the context of modelling. However, the new probability distributions do not admit any closed analytical form of representation. Thus, novel methods need to be developed, as only a few can be found in the literature. Here, we recall a recent novel method, developed by the authors, based on a trigonometric moment estimator using circular distributions. The linear data may be transformed to yield circular data. This transformation is solely for yielding a suitable estimator. Our aim in this paper is to provide a review of the few existing methods, discuss some of their drawbacks, and also provide a universal (∀α∈(0,2]), efficient, and easily implementable estimator of α based on the transformation mentioned above. Novel, circular-statistics-based tests for the index parameter α of the stable and Linnik distributions are introduced and also exemplified with real-life financial data. Two real-life data sets are analysed to exemplify the methods recommended and enhanced by the authors.
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.007 | 0.048 |
| Meta-epidemiology (narrow) | 0.001 | 0.000 |
| Meta-epidemiology (broad) | 0.001 | 0.001 |
| Bibliometrics | 0.004 | 0.003 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.003 |
| Open science | 0.002 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 0.001 |
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 source (direct Gemma or distilled Codex), 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".