QuanTAlib/lib/averages/hma/Hma.md

HMA: Hull Moving Average

Pine Script Implementation of HMA

Overview and Purpose

The Hull Moving Average (HMA), developed by Alan Hull in 2005, is designed to solve the age-old problem of making a moving average more responsive to current price activity while maintaining curve smoothness. It achieves this by eliminating lag almost entirely and managing to improve smoothing at the same time.

Core Concepts

• Lag Reduction: Uses weighted moving averages (WMA) in a specific combination to offset lag.
• Smoothness: The final smoothing step ensures the indicator remains readable and not overly jittery.
• Formula: HMA = WMA(\sqrt{n}, 2 \cdot WMA(n/2, price) - WMA(n, price))

Calculation

1. Calculate a WMA with period n/2 and multiply by 2.
2. Calculate a WMA with period n and subtract from step 1.
3. Calculate a WMA with period \sqrt{n} using the result of step 2.

C# Implementation

using QuanTAlib;

// Initialize
var hma = new Hma(14);

// Update
var result = hma.Update(new TValue(time, price));

// Batch
var series = Hma.Calculate(sourceSeries, 14);

Performance

• Streaming: O(1) complexity per update (uses 3 internal O(1) WMAs).
• Batch: Uses SIMD-optimized WMA calculations and vector operations for the intermediate step.
• Zero Allocation: Span-based API available for high-performance scenarios.

References

• Alan Hull's HMA Description