Average True Range (ATR)

Install and import#

npm install fintech-algorithms

import { averageTrueRange } from "fintech-algorithms/technical-indicators/volatility-and-channels/atr";

Signature#

averageTrueRange(high, low, close, p)

Wilder-smoothed true range. Most often used for position sizing and stop placement rather than as a signal — it says how far price typically moves, not which way.

Parameters#

Returns#

Record<string, (number | null)[]> · length same-as-input

Parallel series: true_range and atr.

Warm-up#

The first p - 1 positions are null. Applies to atr only; true_range is defined from the first bar. The first ATR is the mean of the first p true ranges, so it lands at index p - 1 and Wilder smoothing continues from there.

Errors#

• When p < 1 or is not an integer — throws RangeError
• When the input series are not all the same length — 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#

[101.08, 101.6243955, 102.13058177, 102.56507653, 102.90321818, 103.1320792]

Showing 6 of 240 elements.

[98.92, 99.39457765, 99.83203556, 100.19996391, 100.47473988, 100.64442473]

Showing 6 of 240 elements.

[100, 100.50948657, 100.98130867, 101.38252022, 101.68897903, 101.88825197]

Showing 6 of 240 elements.

14

Call#

averageTrueRange(high, low, close, p)

Returns#

object with 2 fields: true_range, atr

{
  "true_range": [
    2.1599999999999966,
    2.2298178500000034,
    2.298546210000012,
    2.365112620000005,
    2.4284782999999948,
    2.4876544700000096
  ],
  "atr": [null, null, null, null, null, null]
}

Other exports#

This module also exports trueRange. Every module additionally exports run as an alias of its primary function, and a meta object carrying its catalog id, domain, family, shape and article URL.

Diagrams#

Calculation flow#

flowchart LR
    A["True Range stream"] --> B{"n values available?"}
    B -- "no" --> C["ATR = null"]
    B -- "first complete seed" --> D["Arithmetic mean of first n TR"]
    B -- "after seed" --> E["Previous ATR + (TR - previous ATR) / n"]
    D --> F["Directionless price-unit scale"]
    E --> F
    G["Historical revision"] --> H["Recompute every later recursive state"]

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#

• New Concepts in Technical Trading Systems — J. Welles Wilder Jr.
• Average True Range — TA-Lib
• ta_ATR.c — TA-Lib
• True Range — TA-Lib
• Public evidence boundary

The rest of the Volatility and Channels family#

• True RangeThe greater of today's range, the gap up from yesterday's close, and the gap down from it.
• Bollinger BandsA moving average with bands a number of standard deviations away, so the channel widens and narrows with realised volatility.
• Keltner ChannelsAn EMA with bands placed a number of ATRs away.
• Donchian ChannelsThe highest high and lowest low of the lookback.
• Bollinger BandWidthThe width of a Bollinger channel relative to its middle band.