# PRP-36: Mean Reversion Algorithm Implementation
## Context & Motivation
**Integration Goal**: Implement Ornstein-Uhlenbeck process for mean-reverting price generation.
**User Requirement**: Generate synthetic data for mean-reverting assets like pairs trades, forex, and commodities.
**Technical Challenge**: Balance mean reversion strength with realistic price dynamics.
## Requirements
### Mean Reversion Components
1. **Long-Term Mean**: Target equilibrium level
2. **Reversion Speed**: Rate of mean reversion (theta)
3. **Volatility**: Diffusion parameter
4. **Half-Life**: Time to revert halfway to mean
### Algorithm Features
1. **Ornstein-Uhlenbeck Process**: Core mean reversion model
2. **Cointegration Support**: Multiple correlated mean-reverting series
3. **Dynamic Equilibrium**: Time-varying mean levels
4. **Regime Detection**: Identify mean reversion breakdowns
## Implementation Blueprint
### Phase 1: Core Algorithm
1. Create `src/algorithms/mean_reversion.rs`
2. Define `MeanReversionGenerator` struct
3. Implement O-U process discretization
4. Add half-life calculations
### Phase 2: Price Generation
1. Implement drift and diffusion terms
2. Add price path generation
3. Create multi-asset cointegration
4. Test stationarity properties
### Phase 3: Advanced Features
1. Add dynamic equilibrium levels
2. Implement regime detection
3. Create spread generation for pairs
4. Add statistical tests
## Success Criteria
### Validation Gates
```bash
# Test mean reversion
cargo test mean_reversion
cargo test ornstein_uhlenbeck
# Statistical tests
cargo test stationarity_tests
```
### Implementation Metrics
- [ ] Half-life calculation accuracy
- [ ] Stationarity in generated series
- [ ] Cointegration maintained
- [ ] Realistic spread dynamics
## Dependencies & References
**Research Sources**:
- Ornstein-Uhlenbeck process theory
- Pairs trading literature
- Cointegration testing methods
**Mathematical Foundation**:
- dX_t = θ(μ - X_t)dt + σdW_t
- Half-life = ln(2)/θ
- Discretization: X_{t+1} = X_t + θ(μ - X_t)Δt + σ√Δt*Z
**Implementation Patterns**:
- Extend RandomWalkGenerator pattern
- Use similar structure as GARCH
- Integrate with existing generators
## Implementation Tasks
### Phase 1: Basic O-U (2-3 hours)
1. Implement O-U process
2. Add discretization
3. Create half-life calc
4. Write unit tests
### Phase 2: Generation (2-3 hours)
1. Integrate with generator
2. Add parameter config
3. Test mean reversion
4. Validate statistics
### Phase 3: Extensions (2-3 hours)
1. Add cointegration
2. Implement pairs trading
3. Create diagnostics
4. Document usage
## Risk Mitigation
- Validate theta > 0 for stability
- Ensure positive volatility
- Test for stationarity
- Provide calibration tools
## Success Score
**8/10** - Well-understood mathematical model with clear implementation path.