Algorithmic Trading & Indicators Advanced

1D Kalman Filter Zero-Lag Adaptive Trend Tracker in Python NumPy

Implement a 1-Dimensional Kalman Filter in pure Python NumPy as a zero-lag adaptive moving average to filter price noise without window lag.

#numpy#pandas

Problem Statement

Traditional SMAs and EMAs suffer from fixed lookback lag during sharp V-shaped reversals. A Bayesian Kalman Filter updates its state estimate dynamically on every tick based on measurement vs process noise.

Formula / Core Logic

Prediction: x_hat_minus = x_hat_prev, P_minus = P_prev + Q Update: K = P_minus / (P_minus + R), x_hat = x_hat_minus + K * (Price - x_hat_minus)

Installation

pip install numpy pandas

kalman-filter-dynamic-moving-average-hedge-ratio-python.py

import numpy as np
import pandas as pd

def kalman_filter_1d(prices, process_var=1e-5, measurement_var=1e-2):
    n = len(prices)
    xhat = np.zeros(n)
    P = np.zeros(n)
    xhat[0] = prices.iloc[0]
    P[0] = 1.0
    
    for k in range(1, n):
        xhat_minus = xhat[k - 1]
        P_minus = P[k - 1] + process_var
        K = P_minus / (P_minus + measurement_var)
        xhat[k] = xhat_minus + K * (prices.iloc[k] - xhat_minus)
        P[k] = (1 - K) * P_minus
    return pd.Series(xhat, index=prices.index, name='Kalman_Estimate')

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Frequently Asked Questions

Q: How do I make the Kalman curve more responsive to price changes?

Increase `process_var` (Q) or decrease `measurement_var` (R) so the Kalman Gain `K` weights new price observations more heavily.