bitcoin-model/NOTES.md

Bitcoin Price Model Documentation

Model Overview

A probabilistic price projection model combining log returns analysis, cycle awareness, and Monte Carlo simulation. The model generates projected price ranges with confidence intervals, balancing short-term market dynamics with long-term cyclical patterns.

Core Design Principles

1. Return Analysis

• Uses log returns for better handling of exponential growth
• Combines multiple timeframes for volatility estimation
• Implements adaptive window sizing based on market conditions
• Handles volatility clustering through regime-aware adjustments

2. Cycle Integration

• Recognizes Bitcoin's ~4 year (1460 day) halving cycle
• Maps historical returns to cycle positions (0-1 scale)
• Adjusts expectations based on position in cycle
• Handles transitions between cycles with uncertainty scaling

3. Market Era Recognition

Three distinct eras with specific characteristics:

• Early (2013-2017): Higher base volatility, conservative trends
• Transition (2017-2020): Futures market introduction period
• Mature (2020+): Institutional participation, reduced base volatility

4. Uncertainty Estimation

• Generates both point estimates and confidence intervals
• Adapts uncertainty based on market conditions
• Uses asymmetric volatility response
• Implements dynamic confidence interval calibration

Architecture

Key Components

1. Trend Analysis (analyze_trends)

   • Calculates cycle-position-specific returns
   • Applies position-aware smoothing
   • Handles cycle boundaries

2. Volatility Estimation (calculate_volatility)

   • Adaptive window sizing
   • Multi-timeframe integration
   • Era-specific scaling
   • Regime detection and response

3. Price Projection (project_prices)

   • Monte Carlo simulation engine
   • Dynamic uncertainty scaling
   • Confidence interval calculation
   • Trend integration

4. Projection Adjustment (get_projection_adjustments)

   • Time-varying uncertainty scaling
   • Market condition response
   • Cycle position awareness
   • Minimum uncertainty bounds

Model Performance & Validation

Performance Characteristics

Normal Market Conditions

• MAPE: 30-40% typical
• 95% CI Coverage: ~95%
• 68% CI Coverage: ~73%
• Best performance in mature market periods (2020+)
• Most reliable for 3-6 month horizons

Stress Periods

• MAPE: 30-60%
• 95% CI Coverage: ~95%
• 68% CI Coverage: ~76%
• Wider but well-calibrated confidence intervals
• Maintains reliability through increased uncertainty

Key Strengths

1. Consistent confidence interval coverage
2. Rapid adaptation to volatility changes
3. Robust handling of cycle transitions
4. Well-calibrated uncertainty estimates

Known Limitations

1. Higher error during market structure changes
2. Increased uncertainty in early cycle periods
3. Limited incorporation of external factors
4. May underestimate extreme events

Validation Framework

Backtest Configuration

• Minimum training period: 8 years
• Validation period: 2 years
• Rolling window approach
• Separate evaluation of normal/stress periods

Key Test Periods

1. Cycle Transitions

   • Pre/post halving periods
   • Historical halvings (2016, 2020, 2024)
   • Cycle peak/trough transitions

2. Market Structure Changes

   • Futures introduction (2017)
   • Institution adoption (2020-2021)
   • Major market events (e.g., COVID crash)

3. Recent History

   • 2021 bull market
   • 2022 drawdown
   • 2024 recovery

Validation Metrics

1. Accuracy Measures

   • MAPE (Mean Absolute Percentage Error)
   • RMSE (Root Mean Square Error)
   • Maximum deviation

2. Calibration Measures

   • Confidence interval coverage
   • Uncertainty estimation accuracy
   • Regime transition handling

3. Stability Measures

   • Parameter sensitivity
   • Training period dependence
   • Regime change response

Technical Implementation

Core Functions

Volatility Calculation

def calculate_volatility(df, short_window=30, medium_window=90, long_window=180):
    """
    Adaptive volatility calculation combining multiple timeframes.

    Features:
    - Dynamic window sizing based on market conditions
    - Era-specific scaling factors
    - Regime-aware adjustments
    - Robust error handling and fallbacks
    """

Key parameters:

• short_window: Fast response (default 30 days)
• medium_window: Primary estimate (default 90 days)
• long_window: Stability baseline (default 180 days)

Adaptive features:

• Windows shrink in high volatility periods
• Expand during low volatility
• Minimum size constraints for stability
• Weighted combination based on regime

Cycle Position

def get_cycle_position(date, halving_dates):
    """
    Calculate position in halving cycle (0 to 1).
    0 = halving event
    1 = just before next halving
    """

Position calculation:

• Linear interpolation between halvings
• Special handling for pre-first-halving
• Extension mechanism for future cycles
• Built-in boundary condition handling

Price Projection

def project_prices(df, days_forward=365, simulations=1000,
                  confidence_levels=[0.95, 0.68]):
    """
    Generate price projections with confidence intervals.

    Core simulation parameters:
    - Number of paths: 1000
    - Confidence levels: 95% and 68%
    - Dynamic uncertainty scaling
    """

Data Requirements

Input Data

Minimum fields:

• Date
• Close price
• Trading volume (optional)
• High/Low (optional)

Format requirements:

• Daily data preferred
• Sorted chronologically
• No missing dates
• Prices > 0

Training Data

Minimum requirements:

• 2 years for basic operation
• 8 years recommended
• Must include at least one cycle transition
• Should span multiple market regimes

Error Handling

Data Validation

• Missing value detection and interpolation
• Outlier identification
• Zero/negative price handling
• Volume anomaly detection

Runtime Guards

• Minimum data length checks
• Window size validation
• Numerical stability checks
• Regime transition handling

Fallback Mechanisms

1. Simple volatility calculation
2. Default uncertainty estimates
3. Conservative parameter sets
4. Standard cycle assumption

Memory and Performance

Optimization Features

• Efficient numpy operations
• Vectorized calculations where possible
• Smart data windowing
• Caching of intermediate results

Resource Usage

Typical requirements for 10-year dataset:

• Memory: ~100MB
• CPU: ~2-5 seconds per projection
• Storage: Negligible

Parallelization

• Multiprocessing support for backtests
• Independent path simulation
• Multiple period analysis
• Backtest parallelization

Development History & Evolution

Major Versions

Version 1.0 (Initial Implementation)

• Basic log return analysis
• Fixed volatility windows
• Simple cycle position calculation
• Base Monte Carlo simulation

Version 2.0 (Market Structure)

• Added era-based adjustments
• Improved cycle handling
• Multiple timeframe volatility
• Enhanced Monte Carlo engine

Version 3.0 (Current)

• Adaptive volatility windows
• Dynamic uncertainty scaling
• Improved regime detection
• Enhanced confidence interval calibration

Key Improvements

Volatility Estimation

1. Fixed → Adaptive Windows

   • Initial: Fixed 30/90/180 day windows
   • Current: Dynamic sizing based on regime
   • Result: Better regime transition handling

2. Uncertainty Calibration

   • Initial: Fixed scaling factors
   • Current: Market-aware dynamic scaling
   • Result: More reliable confidence intervals

3. Era Recognition

   • Initial: Single model for all periods
   • Current: Era-specific adjustments
   • Result: Better handling of market evolution

Simulation Engine

1. Path Generation

   • Initial: Basic random walks
   • Current: Regime-aware path simulation
   • Result: More realistic price trajectories

2. Confidence Intervals

   • Initial: Fixed width
   • Current: Dynamic, asymmetric intervals
   • Result: Better calibrated uncertainty

Failed Experiments

1. Complex Regime Detection

• Attempted multiple indicator fusion
• Added excessive complexity
• Reduced model stability
• Reverted to simpler approach

2. Machine Learning Integration

• Tested neural network components
• Reduced interpretability
• Inconsistent improvements
• Kept traditional statistical approach

3. External Factor Integration

• Tried incorporating macro indicators
• Added noise to projections
• Complicated parameter estimation
• Maintained focus on price dynamics

Recent Improvements (2024)

Adaptive Volatility Windows

• Implementation: Dynamic window sizing
• Purpose: Better regime handling
• Results:
  • Improved 95% CI coverage to ~95%
  • Better stress period handling
  • More reliable uncertainty estimates

Performance Metrics

Normal Periods:

• MAPE: 39.9%
• RMSE: $12,007
• 95% CI Coverage: 95.9%
• 68% CI Coverage: 72.5%

Stress Periods:

• MAPE: 32.8%
• RMSE: $12,794
• 95% CI Coverage: 95.2%
• 68% CI Coverage: 76.1%

Future Directions

Short Term

1. Fine-tune adaptive parameters
2. Improve transition period handling
3. Enhanced backtest framework
4. Additional regime indicators

Medium Term

1. Cycle strength indicators
2. Volume analysis integration
3. Improved documentation
4. Performance optimization

Long Term

1. Real-time adaptation framework
2. Advanced regime detection
3. Market microstructure integration
4. External API integration