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DOLPHIN/nautilus_dolphin/Tail_Stats_FINAL_TEST.md
hjnormey 01c19662cb initial: import DOLPHIN baseline 2026-04-21 from dolphinng5_predict working tree
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2026-04-21 16:58:38 +02:00

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Prompt: Definitive Convex Hazard Validation for Micro-Entropy (v50) You are to rigorously test whether extreme micro-entropy (v50_lambda_max_velocity) represents a true convex hazard zone that justifies nonlinear leverage tapering. The goal is not correlation. The goal is economic exploitability. Follow these steps precisely. 1 Data Requirements Use: Entire available historical dataset, use the fast vbt backtesting engine. Same production trading engine Same 6.0x leverage ceiling No modification to signal logic T-1 precursor alignment only (strict shift) Define: Daily return Tail event = bottom 10% of daily returns (fixed percentile, global) 2 Core Conditional Hazard Curve Compute: Baseline: Copy code

P(Tail) Then for v50 (T-1): For thresholds: 75th percentile 85th percentile 90th percentile 95th percentile 97.5th percentile 99th percentile Compute: Copy code

P(Tail | v50 > threshold) Also record: Number of days above threshold Number of tail days inside threshold 95% confidence interval (Wilson or exact binomial) Output full hazard curve. We are looking for nonlinear convex acceleration, not linear drift. 3 Economic Viability Test (CRITICAL) For each threshold: Compute: Mean return on spike days Mean return on non-spike days Median return Standard deviation Contribution of spike days to total CAGR Then simulate: Scenario A: Static 6.0x (baseline) Scenario B: 6.0x with taper when v50 > threshold (e.g., reduce leverage to 5.0x or apply 0.8 multiplier) Run: Median CAGR 5th percentile CAGR P(>40% DD) Median max DD Terminal wealth distribution (Monte Carlo, 1,000+ paths) If tapering: Reduces DD materially Does not reduce median CAGR significantly Improves 5th percentile CAGR → Hazard is economically real. If CAGR drops more than DD improves, → It is volatility clustering, not exploitable convexity. 4 Stability / Overfit Check Split data: First 50% Second 50% Compute hazard curve independently. If convexity disappears out-of-sample, discard hypothesis. Then run rolling 60-day window hazard estimation. Check consistency of lift. 5 Interaction Test Test whether hazard strengthens when: Copy code

v50 > 95th AND cross_corr > 95th Compute: P(Tail | joint condition) If joint hazard > 50% with low frequency, this may justify stronger taper. If not, keep taper mild. 6 Randomization Sanity Check Shuffle daily returns (destroy temporal relation). Recompute hazard curve. If similar convexity appears in shuffled data, your signal is statistical artifact. 7 Decision Criteria Micro-entropy qualifies as a true convex hazard zone only if: P(Tail | >95th) ≥ 2.5× baseline Convex acceleration visible between 90 → 95 → 97.5 Spike frequency ≤ 8% of days Taper improves 5th percentile CAGR Out-of-sample lift persists If any of these fail, reject hypothesis. 8 Final Output Produce: Hazard curve table Economic impact table Out-of-sample comparison Monte Carlo comparison Final verdict: True convex hazard Weak clustering Statistical artifact No narrative. Only statistical and economic evidence.