Audited / PhD Validated · Two Independent Reports
Audited & PhD Validated
Two independent PhD reviews of RegimeSignal™'s four S&P 500 prediction signals — the full market cycle. Both reached the same determination: "Validated with Qualifications," with every limitation disclosed in full below.
Independent PhD Validation · Report 1 of 2
Full Market Cycle Prediction, Validated
An independent PhD statistical validation of RegimeSignal™'s four S&P 500 prediction signals — the full market cycle: pullback, correction, bear, and recovery. Reviewer: Dr A. Trabelsi Karoui, PhD · June 2026.
PhD Independent Validator
Dr Ali Trabelsi Karoui, PhD
PhD in Finance · University of Sfax (2023) · Master's in Research (Finance), École Supérieure de Commerce, University of Sfax (2018)
R&D Team Lead, Financial Innosights · Data Scientist, FundEvolve · former Postdoctoral Researcher, ICADE Business School, Universidad Pontificia Comillas (Madrid).
Peer-reviewed publications in ranked finance journals, with research spanning regime modeling, market-stress indices, exchange-rate econometrics, and applied machine learning in finance (Best Paper Award, International Finance Conference, 2024).
His hands-on methodological expertise maps directly onto what these signals use: walk-forward (expanding-window) backtesting and out-of-sample evaluation, regularized linear and non-linear ensemble classifiers, confusion-matrix and AUC/precision–recall analysis under class imbalance, bootstrap robustness testing, and Markov regime-switching models.
The engagement
RegimeSignal™ commissioned a fully independent statistical validation and replication of its four classifier signals from a doctoral quantitative-finance researcher with no role in the models' construction. The reviewer worked from a locked evaluator package — code, locked prediction files, data, and a SHA-256 manifest — over a defined review window (May 30 – June 3, 2026), reinstalling the environment from scratch and re-running every reproduction script.
Scope & protocol
Four classifier signals were in scope — BRS, MBS T1, MBS T2, RRS. The Bull/Bear Velocity gauges, the HybridBrain™ overlay, and the AI assistant were out of scope. The protocol covered five areas: (a) package-integrity verification against the SHA-256 manifest, (b) reproduction of every headline confusion matrix, (c) walk-forward protocol integrity (look-ahead / leakage), (d) input-data integrity via FRED spot-checks, and (e) a methodology assessment against known statistical failure modes.
Findings by area
Reproduced precision & confidence intervals
| Signal | Precision | Wilson 95% CI |
|---|---|---|
| BRS — Bear regime (−20%) | 86% | 72% – 93% |
| MBS T1 — Pullback (−5%) | 83% | 69% – 92% |
| MBS T2 — Correction (−10%) | 84% | 68% – 93% |
| RRS — Recovery (+10%) | 82%* | 52% – 95% |
All four confusion matrices reproduced exactly from the locked files; MBS T1, MBS T2 and RRS matched to floating-point tolerance, and every walk-forward fire/no-fire decision was identical. Intervals reflect genuine sampling uncertainty given the modest number of historical signal events — widest for RRS, which fired only 11 times in its out-of-sample window. *See qualifications.
All four published confusion matrices reproduced exactly from the locked files. The methodology was judged sound for the Bear Regime Signal and both Market Break tiers. The qualifications — disclosed in full below — pertain principally to the Regime Recovery Signal and to two macro-guardrail data gaps, and were themselves pre-disclosed by the author as the reason for commissioning the report.
⚠ Qualifications, disclosed in full
Regime Recovery Signal (RRS). Its decision threshold and hyperparameters were selected on the same out-of-sample window on which its results are reported, so its precision is a historical upper bound under an optimized operating point, not an unbiased forward estimate — with a wide confidence interval (52%–95%). Pre-disclosed by the author.
BRS guardrail data gaps. Two of the eight macro guardrails (a high-yield credit-spread series and a forward P/E series) had data gaps and defaulted to PASSED for much of the out-of-sample history, so the two-layer system effectively operated with roughly six of eight guardrails. The direction of both defaults is conservative — they cannot inflate false positives, only reduce coverage.
BRS coverage. Bear-Alert recall is intentionally secondary by design (high precision comes at the cost of some missed bear months at the Alert level); broader coverage is supplied by the velocity gauges and lower-tier watch alerts, which were out of scope.
Determination is "Validated with Qualifications," not an unconditional validation. Full report available to qualified reviewers under NDA on written request to info@cronusmarketintelligence.com. This review does not validate live or production deployment, and does not constitute investment advice. Past market signal record does not guarantee future results.
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.
Early warning, before consensus.
Is a crash or correction coming? Ask the model — free for 15 minutes, no signup.
The RegimeSignal™ framework — four walk-forward validated prediction signals and Bull / Bear Velocity gauges for the S&P 500. Start your 7-day free trial today.
Cancel anytime — no contracts, no early-termination fees