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Calculate Hull Moving Average (HMA) for Zero-Lag Trend Following in Python

Compute Alan Hull's High-Speed Hull Moving Average (HMA) in Python Pandas, eliminating lag while maintaining exceptional smoothness.

#pandas#numpy

Problem Statement

Simple and Exponential Moving Averages suffer from severe lag during rapid price acceleration. The Hull Moving Average solves lag entirely using weighted WMA math.

Formula / Core Logic

HMA = WMA(2 * WMA(n/2) - WMA(n), sqrt(n))

Installation

pip install pandas numpy

hull-moving-average-hma-zero-lag-python.py

import pandas as pd
import numpy as np
\.def calculate_hma(df, period=16):
    def wma(ser, p):
        weights = np.arange(1, p + 1)
        return ser.rolling(p).apply(lambda x: np.dot(x, weights) / weights.sum(), raw=True)
        
    half_p = int(period / 2)
    sqrt_p = int(np.sqrt(period))
    wma_half = wma(df['Close'], half_p)
    wma_full = wma(df['Close'], period)
    diff = (2 * wma_half) - wma_full
    hma = wma(diff, sqrt_p)
    df['HMA'] = hma
    return df

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Frequently Asked Questions

Q: Why does HMA have zero lag compared to EMA?

By subtracting a weighted moving average of half period from full period and smoothing by square root, HMA mathematically cancels out lag.