PLANNED · implementation
Hypothesis
Following Sornette's Log-Periodic Power Law model, financial bubbles exhibit faster-than-exponential growth with log-periodic oscillations preceding a critical time tc. We test whether crypto's accelerated bubble cycles (days–weeks rather than months) yield tractable tc predictions on BTC, ETH, and top alts.
Math — Sornette LPPL
$$ \ln p(t) = A + B(t_c - t)^{m} + C(t_c - t)^{m} \cos\left(\omega \ln(t_c - t) - \phi\right) $$
Parameter ranges from Sornette's published constraints:
m∈ [0.1, 0.9] — critical exponent (typically 0.33)ω∈ [6, 13] — log-periodic frequency (typically 6.36)tc— critical time (singularity), constrained to next 1–14 daysA, B, C, φ— fit parameters via Levenberg-Marquardt
Plan
- Rolling LPPL fit on 1h log-prices, window 30–90 days, refit every hour
- Validity gates: 0.1<m<0.9, 6<ω<13, R²>0.9, tc within 1–14 days forward
- Parameter stability check across multiple window shifts
- Multi-asset confluence (3+ synchronous bubble signals = strong)
- Entry: SHORT setup 2–5 days before tc
- Exit: at tc or on LPPL fit breakdown
Prior art
- Sornette (1996–present), Financial Crisis Observatory, ETH Zurich
- 27+ peer-reviewed papers documenting fits on major historical bubbles (1929, 1987, 2000, 2007)
- Mixed crypto results: BTC 2017 and 2021 peaks fit well ex-post; out-of-sample mixed
Implementation queued. Edge probability estimated 30–50% based on Sornette's published track record. Crypto-specific high-frequency LPPL with multi-asset confluence has no public retail-grade implementation we are aware of.