Summary
Shannon Entropy Market Analysis - Phase 2 applies information theory to live data (Feb 2026), quantifying trader behavior complexity through entropy (0.0-1.585 bits range).
Key discovery: Low entropy leads to high volatility - 0.599 bits leads to 4.999+ volatility spikes. the Correlation is r=-0.193 (negative) and reveals a crash predictability pattern.
This is a behavioral measurement framework validated end-to-end on real market data, and not a trading strategy.
Core Contributions (Sole Creator)
Verified components:
- Live Pipeline - Data processing, 3-panel visualization (correlation, time-series, stats)
- Entropy Engine - Theoretical max 1.585 bits achieved; Phase 2: 0.599 (crash) to 1.50 (normal)
- Rolling Window Analysis - 100-period entropy vs 10-period volatility std dev
- Behavioral Regime Detection - Clear signatures: crashes vs stable vs volatile normal
Behavioral Interpretation
Entropy as Market Stress Index:
- Low entropy (0.0-0.6 bits): Crash regime → 4.999+ volatility
- Medium entropy (1.2-1.5 bits): Normal volatile → 173-178 volatility
- Zero entropy (0.000 bits): Stable periods → 0.000 volatility
Correlation: r=-0.193 confirms low entropy → high volatility across 60 market scenarios.
Validation Results
Live Pipeline:
Live Analysis (Feb 2026) Records processed: 100% success Entropy range: 0.000 - 1.50 bits Volatility range: 0.000 - 191.424 Correlation: ρ = -0.193 (negative) Crash detection: 0.599 bits → 4.999+ vol
Mathematical correctness:
- Theoretical maximum entropy confirmed (1.585 bits, 3 trader actions)
- Edge cases validated: no variance, and uniform distributions
- 60 market scenarios: crash / normal / volatile regimes distinguished
Technical Validation
- Language: C++17 core + Python visualization
- Data: Live SPY CSV (c,h,l,o,dp,t)
- Entropy: Shannon H = -Σ(pᵢlog₂pᵢ), 100-period rolling
- Volatility: Price std dev, 10-period rolling
- Visualization: 3-panel PNG output (scatter, entropy/volatility series)
- Correlation: Pearson ρ = -0.193
Current Status
- Live pipeline
- Entropy/volatility regime signatures
- Negative correlation (r=-0.193)
- Crash predictability pattern
Ongoing Research:
- HFT co-location (millisecond executions) most likely wont happen in the close future.
- Semi-supervised to unsupervised learning models. With the addition of regression/trees & Reinforcement Learning methods.
- Real exchange order flow integration
Final Insight
Low entropy leads to high volatility. r=-0.193 reveals crash predictability.
Requires co-located HFT model near exchange for millisecond execution validation.