Shannon Entropy Market Analysis

Summary

Shannon Entropy applies information theory to quantify trader behavior unpredictability. Initial testing on synthetic data reveals patterns worthy of further investigation, though results require validation with real market data.

Key Findings

Counterintuitive Market Patterns:

Panic/FOMO Events: Low entropy (0.0 bits) + High volatility spike (4.5-5.0)
Mixed Sentiment: High entropy (1.5+ bits) + Moderate volatility (2.8-3.2)
Chaotic Trading: High entropy (1.5+ bits) + Very high volatility (4.8+)

Core Insight: Synthetic data shows entropy and volatility have negative correlation (-0.602); this contradicts the initial hypothesis and requires real-world testing to understand the relationship.

Technical Implementation

Core Entropy Calculation:

 1
 2
 3
 4
 5
 6
 7
 8
 9
10
11
12
13
double shannon_entropy(std::vector<int> actions) {
    std::map<int, int> counts;
    int total = actions.size();
    for (int action : actions) {
        counts[action]++;
    }
    double entropy = 0.0;
    for (auto& pair : counts) {
        double p = (double)pair.second / total;
        if (p > 0) entropy -= p * std::log2(p);
    }
    return entropy;
}

Validation Results:

Unit Tests: 100% pass rate (exact entropy calculations)
Robustness Tests: 15/15 edge cases handled
Market Validation: 25 windows across 5 scenarios; entropy-volatility correlation: -0.602 (negative, not positive as hypothesized)
Mathematical Accuracy: Achieves near-theoretical maximum entropy (1.58+ bits); minor deviations (<0.06 bits) in specific distributions

Research Applications (proposed needs validation)

Risk Management: Behavioral pattern detection, low entropy with high volatility observed in panic/FOMO scenarios; requires real market data validation before use as crash predictor Market Timing: Entropy as a market state complexity indicator; temporal relationship between entropy changes and volatility spikes requires a time series analysis (not yet tested) Behavioral Analysis: Successfully quantifies trading action distribution complexity; validated against synthetic behavioral patterns (hold/buy/sell actions) Trading Strategy: Entropy-based market analysis framework; current negative correlation (-0.602) between entropy and volatility suggests an inverse relationship strategy, which requires model revision and real-world backtesting before practical application.

Methodology

Data Collection: Trader actions (0=hold, 1=buy, 2=sell) Time Windows: Sequential trading periods Entropy Formula: H = -Σ(p_i * log2(p_i)) Testing Framework: Unit tests, robustness tests, market simulation, visual validation

Current Status

Research Phase: Theoretical framework validated with simulated data Next Steps: Testing on real market data from major exchanges Limitations: Has yet to be tested on real-time market data

Repository Structure

Shannon-Entropy/
├── data-collection.cpp          # Core entropy function
├── tests/                       # Comprehensive test suite
├── visualize_entropy.py        # Python visualization
├── requirements.txt            # Python dependencies
└── setup.sh                   # Environment setup

References

Shannon, C.E. (1948). “A Mathematical Theory of Communication”
Information Theory in Behavioral Finance
Market Microstructure and Entropy Analysis