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Kalman Filter Trend
Use a 1D Kalman filter to estimate the latent price trend; trade in the direction of the filter.
Strategy briefing
Understand what this strategy is actually betting on before you touch the parameter panel.
Use category and difficulty as context
Compare before optimizing
Map the strategy to a regime thesis
Read the math as a constraint system
Use parameters to test fragility, not creativity
Learning linkup
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Validation & skepticism
The Intuition
The Kalman filter, developed by Rudolf Kálmán (1960), is a recursive Bayesian estimator for the hidden state of a linear dynamical system observed with noise. In trading, we treat the true latent price trend as the hidden state, and the observed price as a noisy measurement of that state. The filter optimally combines the prior state estimate with the new observation, weighted by their relative uncertainties.
The key innovation over simple moving averages: the Kalman gain K(t) is adaptive. When observations are very noisy (high R) relative to the state process noise (Q), K is small — the filter trusts its prior prediction more than the new data. When observations are relatively reliable, K is large — the filter updates heavily on the new price. This makes the Kalman filter a self-calibrating smoother that is optimal in the least-squares sense under Gaussian assumptions.
In equities and futures, the Kalman filter has been used for: (1) Pairs trading — estimating a time-varying hedge ratio between two assets (Chan 2013); (2) Kalman-smoothed trend signals — the filtered state estimate is a more principled trend estimate than a fixed-window moving average; (3) Online regression — the filter can track the OLS relationship between two series in real time without a fixed window.
Key assumptions: (1) The system is linear: the state transition (x(t) = x(t-1) + w) and observation model (z(t) = x(t) + v) are both linear. (2) Noise is Gaussian: process noise w and observation noise v follow normal distributions. (3) Q and R are correctly specified. In practice, these noise variances must be estimated or tuned — wrong values give systematically over- or under-reactive filters. (4) The state dimension is appropriate — our 1D filter tracks a single latent price level; real implementations often use 2D state (level + trend).
The main failure mode: if Q/R is too high (too much trust in the state model), the filter is slow to respond to genuine price moves — it lags badly. If Q/R is too low, the filter is very noisy and essentially tracks the raw price. Tuning Q and R is an empirical problem; many practitioners use expectation-maximisation (EM) algorithms to estimate them from the data. Without careful calibration, Kalman filter trading signals can underperform simple moving averages.
The Math
Read this as a compact model summary: what the signal sees, what it ignores, and where fragility can creep in.
State: x(t) = x(t-1) + w(t), w ~ N(0, Q)
Obs: z(t) = x(t) + v(t), v ~ N(0, R)
Predict: x̂(t|t-1) = x̂(t-1)
P(t|t-1) = P(t-1) + Q
Update: K(t) = P(t|t-1) / (P(t|t-1) + R)
x̂(t) = x̂(t|t-1) + K(t) × (z(t) - x̂(t|t-1))
P(t) = (1 - K(t)) × P(t|t-1)
Signal(t) = +1 if Δx̂(t) > 0 [trend rising]
= -1 if Δx̂(t) < 0 [trend falling]
Parameters
| Parameter | Type | Default | Description |
|---|---|---|---|
| process_noise | float | 0.0001 | Kalman process noise variance (Q) |
| obs_noise | float | 0.01 | Kalman observation noise variance (R) |
Source Code
Live source — fetched from engine/strategies/kalman.py
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Further Reading
- Kalman, R. (1960). A New Approach to Linear Filtering and Prediction Problems. ASME Journal of Basic Engineering, 82(1), 35–45.
- Chan, E. (2013). Algorithmic Trading, Ch. 6. Wiley.
- Welch, G. & Bishop, G. (2006). An Introduction to the Kalman Filter. UNC Technical Report TR 95-041.
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