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.
Two independent reports
A second, stricter independent report followed.
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.