The Anomalous Behavior of Stock Prices on the Canadian Securities Exchange
Bibliographic record
Abstract
This paper examines the conformity of the distribution of stock prices on the Canadian Securities Exchange (CSE) to that theorized by Benford’s Law (BL). BL follows a logarithm law such that the leading digits have a higher probability of lower numbers such as 1, 2, or 3 versus higher numbers like 7, 8, or 9. This analysis can be used to detect fraudulent manipulation of stock prices. Previous research has applied BL to a broad range of data such as cost data, atomic weights, river areas, and populations, as well as stock prices. After collecting stock prices on the CSE, the number count for each digit was compared to the expected number given the frequencies posited by BL. A chi-square test was employed to determine statistical significance. The first digit was found to adhere to BL; however, the second digit was not congruent with that predicted by BL. There is an indication of possible manipulation on this stock exchange. These mixed results are consistent with the empirical evidence of other researchers. This evidence is relevant to auditors, shareholders, financial analysts, investment managers, government, and the CSE.
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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 | 0.001 | 0.024 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.004 | 0.005 |
| Science and technology studies | 0.002 | 0.001 |
| Scholarly communication | 0.002 | 0.001 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.000 | 0.001 |
| Insufficient payload (model declined to judge) | 0.002 | 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 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".