Hull Moving Average

Classic moving-average low-lag smoothing classic

The Hull Moving Average (HMA) aims to reduce lag while maintaining smoothness.

Visual Example

Hull Moving Average — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-07-01 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

The Hull Moving Average (HMA) aims to reduce lag while maintaining smoothness.

Use as a near-zero-lag moving average for trend-following systems where entry timing is critical. The HMA substantially reduces the lag of a same-period WMA.

Native Rust implementation with gold-standard or TA-Lib parity tests where applicable.

Alan Hull designed the Hull Moving Average to nearly eliminate lag while maintaining smoothness. It achieves this by computing a WMA of doubled period, subtracting a WMA of full period, then applying a final WMA to the difference over the square-root period, combining speed with noise reduction. — AlanHull.com

Typical applications:

Trend filter or signal line for systematic entries
Default lookback 14 — tune per asset volatility
Cross with faster oscillator for entry timing
Streaming and Polars paths are bit-identical for production parity

QuantWave implements this via the universal Next<T> trait — bit-identical across Rust streaming, Python streaming, and Polars .ta() batch plugins.

Formula / Specification

Implementation (quantwave-core/src/indicators/hma.rs):

\[ HMA = WMA(2 \times WMA(\frac{n}{2}) - WMA(n), \sqrt{n}) \]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/hma.json.

Parameters

Parameter	Default	Description
`period`	14	Smoothing period

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::HMA;
use quantwave_core::traits::Next;

let mut ind = HMA::new(14);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import HMA

ind = HMA(14)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_hull_moving_average(series: pl.Series) -> pl.Series:
    ind = qw.HMA(14)
    return pl.Series([ind.next(float(v)) for v in series.to_list()])

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").map_batches(apply_hull_moving_average, return_dtype=pl.Float64).alias("hull_moving_average")
    )
    .collect()
)

All surfaces are bit-identical via the single Next<T> implementation and proptests.

Edge Cases & Limitations

Warm-up: first 14 bars may return NaN or partial state per implementation.
Parameter sensitivity: smaller periods increase noise; larger periods increase lag.
Sudden gaps or bad ticks can distort rolling windows — consider pre-filtering.
Single-series indicators ignore volume unless otherwise documented.
Validated via proptests against gold-standard vectors where available.
No look-ahead bias; streaming and Polars batch paths are bit-identical.

Boundary Behavior

Condition	Behavior
Warm-up	Leading bars return NaN until warmup_bars is satisfied.
period > len	When period exceeds series length, output is all NaN.
NaN inputs	NaN in input propagates to output (NaN out).
Invalid params	Non-positive period or missing required params raise ValueError.
Empty data	Empty input returns an empty result series.

Sources & References

Primary Source: https://alanhull.com/hull-moving-average

Implementation: quantwave-core/src/indicators/hma.rs (HMA / HMA_METADATA). Parity: quantwave-core/tests/gold_standard/hma.json

Provenance: Standards bulk upgrade 2026-07-01 IST — see docs/DOCUMENTATION_STANDARDS.md.