Overview
The Kalman filter is a recursive Bayesian estimator used to infer a latent, smoothed state (such as an underlying trend level) from a sequence of noisy price observations. It is used within the eXpeed Research Lab framework as an alternative structural reference line to the wavelet-based approach, and as a component in state-space models of price dynamics.
Mathematical Formulation
The filter assumes a linear state-space system: a state equation describing how the latent state evolves over time subject to process noise, and an observation equation relating the noisy observed price to the latent state subject to measurement noise. At each step the filter performs a predict phase, projecting the prior state forward, followed by an update phase that corrects the prediction using the new observation, weighted by the Kalman gain. The gain balances confidence in the model’s prediction against confidence in the new observation, based on their respective noise covariances.
Application to Trading
As with the wavelet line, the Kalman-filtered series functions as a stable reference line for structural comparison against price. Multi-timeframe display (e.g. computing the filter on a higher timeframe and projecting it onto a lower-timeframe chart with correct bar-time alignment) is used to avoid repaint while providing a steadier reference than a same-timeframe filter would.
A Note on Marketing Claims
Kalman filtering (often combined with parameter optimizers such as particle swarm optimization, PSO) is a legitimate and long-established technique in state-space modeling of financial series. It is also, however, one of the more common pieces of technical vocabulary used in low-substance social media marketing of trading systems. Claims of stable 90%+ “accuracy” across short verification windows, without disclosed methodology, sample size, drawdown, or realized P&L net of costs, should be treated with default skepticism regardless of which model name is attached to them. In internal testing, honestly reported direction accuracy on short horizons (for example 4-hour BTCUSD direction) has been close to 50%, consistent with near-random-walk behavior rather than any claimed edge.
Limitations
Filter performance depends heavily on the assumed noise covariances, which are rarely known in advance and are typically tuned on historical data, introducing the same overfitting risk as any other parametric model. State estimates lag during genuine regime transitions, and forward (walk-forward) validation on unseen data is necessary before treating any backtested accuracy figure as representative of live performance.
Related
Math Models · Wavelet Transform · ARIMA · GARCH · Methodology