The Occurrence of Fibonacci Numbers in Time Series of Financial Accounting Ratios: Anomalies or Indicators of Firm Survival, Bankruptcy and Fraud? An Exploratory Study
Bibliographic record
Abstract
Although there have been conjectures about the possible occurrences of Fibonacci numbers and golden means and ratios in financial statements (Feroz, 1992), it is intriguing as to why managers should be reporting these rather stylized series of numbers the occurrences of which have hitherto been documented mostly in the biological sciences (Davis, 1989). One possible explanation is that these numbers are merely random occurrences and are not a part of any systematic financial reporting pattern. Still other conjectures are that these numbers are generated by a process of skilful manipulation of accounting rules (e.g. smoothing) which has been documented in the empirical accounting literature (Healy, 1985). The purpose of this study is to empirically verify the null hypothesis that the occurrence of Fibonacci numbers, golden ratio and means in financial accounting ratios, is merely a random occurrence without any statistical significance. We constructed two samples: a random sample of 200 companies, and another sample of 200 companies that have survived 20 years or more. We find that i) there is an infinity of distributions under which the null hypothesis (Ho) cannot be rejected for either sample; and ii) there is an infinity of distributions under whichH0 cannot be rejected for the sample of 200 surviving companies but can be rejected for random sample. The latter result is particularly important because it shows that it is possible to discriminate between surviving companies and randomly selected companies based on the golden mean in total debt/total invested capital ratio. © MCB UP Limited 2000.
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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 | 0.005 | 0.031 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.003 | 0.003 |
| Science and technology studies | 0.000 | 0.002 |
| Scholarly communication | 0.001 | 0.002 |
| Open science | 0.001 | 0.001 |
| Research integrity | 0.001 | 0.001 |
| 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 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".