Quantitative methods · Advanced · Daily
Hawkes Process Jumps
How it works, and when it doesn't.
Kalman-smoothed price series has ~40% less noise than a 20-day SMA while maintaining similar trend detection speed. The filter's innovation covariance provides a natural confidence measure.
Holding SPY
Hawkes intensity=0.000 (low, 82% pct). Last jump=4d ago. μ=0.000, α=0.990, κ=5.000. Low jump risk — safe to enter long in bull trend.
Why it works
The Kalman Filter extracts the true underlying trend from noisy price data using an optimal recursive Bayesian estimator. Unlike simple moving averages, it adapts its smoothing parameter in real-time based on the signal-to-noise ratio. The EM algorithm optimizes filter parameters weekly on recent data.
The signal logic
- Fit Kalman Filter to price series with EM-optimized parameters
- Compute Kalman trend velocity (1st derivative of smoothed price)
- Long when velocity > 0 and accelerating (2nd derivative > 0)
- Short when velocity < 0 and decelerating
- Confidence from Kalman innovation covariance (uncertainty estimate)
When it fails
Sideways choppy markets cause frequent signal reversals as the filter mistakes noise for trend changes.
- Best market
- Sustained directional trends where Kalman velocity stays consistently positive/negative
- Worst market
- High-frequency oscillating markets that confuse the filter's state estimate
Backtest
| Sharpe ratio | 0.71 |
| Annual return | 6.7% |
| Worst drawdown | -9.1% |
| Trades in the backtest | 32 |
Backtest on daily bars, positions taken the bar after the signal (no look-ahead).
Hawkes Process Jumps, live.
Re-scored after every close.
The platform runs this and 32 other strategies against the live tape each day — with the evidence behind every number.