Hull MA

Install and import

bash

npm install fintech-algorithms

import { calculateHullMa } from "fintech-algorithms/technical-indicators/trend-smoothing/hull-ma";

Signature

calculateHullMa(values, window)

Hull moving average: a weighted combination of two WMAs de-lagged against each other, then re-smoothed over sqrt(window). Far more responsive than an SMA of the same length, at the cost of overshoot.

Parameters

Name	Type	Notes
`values`	`(number \| null)[]`	Observation series in chronological order, oldest first. nulls: propagate
`window`	`number`	Base window; the internal halved window and the sqrt(window) smoothing window derive from it. min: 1 · integer: true

Returns

(number | null)[] · length same-as-input

Smoothed series, null during the combined warm-up of all three stages.

Warm-up

The first window + ceil(sqrt(window)) - 2 positions are null. Warm-up positions are null rather than a partial result, so a consumer never mistakes an incomplete window for a real value.

Errors

When window < 1 or is not an integer — throws RangeError

Complexity: time O(n), space O(n).

Worked example

executed Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

Input

values

[10, 13, 12, 15, 14, 18]

Showing 6 of 10 elements.

window

Call

calculateHullMa(values, window)

Returns

object with 6 fields: halfLength, rootLength, shortWma, longWma, rawHull, hullMa

{
  "halfLength": 2,
  "rootLength": 2,
  "shortWma": [null, 12, 12.333333333333334, 14, 14.333333333333334, 16.666666666666668],
  "longWma": [null, null, null, null, 13.466666666666667, 15.2],
  "rawHull": [null, null, null, null, 15.200000000000001, 18.133333333333336],
  "hullMa": [null, null, null, null, null, 17.15555555555556]
}

Diagrams

Calculation flow

Hull MA calculation flow

flowchart TD
    A["Validated ordered source x(t)"] --> B["Short WMA: h = floor(n / 2)"]
    A --> C["Long WMA: n observations"]
    B --> D{"Both WMAs ready?"}
    C --> D
    D -- "No" --> E["Emit aligned null raw value"]
    D -- "Yes" --> F["Raw Hull: R(t) = 2 × short − long"]
    F --> G["Collect r = floor(sqrt(n)) consecutive raw values"]
    G --> H{"Final WMA window ready?"}
    H -- "No" --> I["Emit aligned null HMA"]
    H -- "Yes" --> J["HMA(t) = WMA(r) of raw Hull"]
    J --> K["Publish components, lengths, policy, and provenance"]

How it works

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References

Primary definition
Independent confirmations
Canonical decisions
Independent derivations
Historical-example evidence gate
Non-claims