Independent PhD Audit · Report 2 of 2
Independently audited — all four signals across the full S&P 500 market cycle
~86%
bear-market precision · flagship BRS · reproduced exact
✓ Genuine signal, confirmed. Across 1,000 shuffled-label trials, all four signals scored far above random chance — zero matched the real model.
A deliberately stricter, independent PhD replication and robustness audit of RegimeSignal™'s four S&P 500 prediction signals — the full market cycle — designed not to duplicate the validation. Auditor: Dr Jamal Hossain, PhD · July 8, 2026.
PhD Independent Auditor
Dr Jamal Hossain, PhD
Lecturer in Applied Health Statistics · University of Southampton
PhD · MSc, Statistics (with distinction) · BSc (Hons), Statistics · FHEA · Member, Statistical Sciences Research Institute (S3RI)
PhD in Social Statistics & Demography (University of Southampton, 2023), completed as a Commonwealth Scholar. Peer-reviewed publications in journals including JAMA Network Open and PLoS ONE, with research spanning statistical modelling, multilevel & longitudinal analysis, classification metrics, reproducibility, and machine-learning methods. ORCID: 0000-0002-2728-1055.
Four signals across the full cycle
BRS — Bear market (−20%)
−20% · audit-clean
MBS T1 — Pullback (−5%)
−5% · audit-clean
MBS T2 — Correction (−10%)
−10% · audit-clean
RRS — Recovery (+10%)
+10% · exploratory*
| Signal | Precision | AUC | Repro |
|---|---|---|---|
| BRS — Bear market (−20%) | 85.7% | 0.91 | Exact |
| MBS T1 — Pullback (−5%) | 83.3% | 0.88 | Bit-exact |
| MBS T2 — Correction (−10%) | 84.4% | 0.92 | Bit-exact |
| RRS — Recovery (+10%) | 81.8%* | 0.76 | Exact |
What the audit confirmed
- ✓Every signal sits far above the permutation-null baseline — genuine signal, not artifact.
- ✓Benchmarked against three independent alternative learners on identical data — all within a tight AUC band; one scored marginally higher. Results are not algorithm-picked.
- ✓Three of four signals (BRS, MBS T1, MBS T2) reproduced audit-clean and well-supported on the out-of-sample record.
- ✓All 35 locked files checksum-verified and matched; four signals reproduced with no divergence.
- ✓MBS T1 and MBS T2 reproduced bit-exact (~1×10⁻⁸; every one of 154 fire/no-fire decisions).
- ✓No feature-level label leakage — the predicted month is excluded and features are lagged one month.
- ✓The Market Break signals degrade gracefully under a 12-month cutoff shift.
⚠ Qualifications — disclosed in full
RRS — real signal, conservative claim. RRS cleared the same chance test, so the signal is genuine. The one caveat is narrow: its 82% was measured on the window used to tune it, so we publish it as a historical upper bound and treat ~69% as the honest prospective estimate. Precision-first · recall ~39% by design.
Small event counts across all signals (67 / 46 / 33 / 23) — bands are wide. No purge/embargo for the 4-month label horizon; BRS reproduced on a locked Layer-1 composite.
* RRS 82% = 9 of 11 fires correct at the locked high-conviction threshold, reproduced exactly. Because the threshold was chosen on the reported window, it is in-sample-optimistic; prospective estimate ~69% (Wilson 95% CI ≈ [0.52, 0.95]). Presented as exploratory pending out-of-sample data postdating the lock.
Full report available to qualified reviewers under NDA on written request to info@cronusmarketintelligence.com.
Independent review of the documented walk-forward methodology and reproducibility of the headline confusion matrices from locked artifacts as of June 3, 2026. Not an opinion on future results; does not validate production deployment; not investment advice. Past statistical results are not indicative of future results.