Arnaud Legoux Moving Average (ALMA)

Summary

Arnaud Legoux Moving Average: the last N inputs weighted by a Gaussian whose peak sits a fraction offset of the way from the oldest to the newest bar. Moving the offset toward 1 puts the peak on recent bars and cuts the lag; moving it toward 0 puts the peak on old bars and lags most. Smoothing is greatest with the peak mid-window, near 0.5. Sigma sets the width: the Gaussian's standard deviation is N / sigma bars, so a larger sigma concentrates the weight around the peak and smooths less.

The weights are non-negative and sum to one, so the line stays within the range of its window, up to rounding. At the default shape and a period of 5 or more, it lags about half as much as an SMA of the same period and passes about twice its noise.

Chart

Reference data (CSV) · Chart (SVG)

Chart metadata i

Outputs

• outReal: line

Formula

N = optInTimePeriod, m = floor( offset * (N-1) ), s = N / sigma

g[j] = exp( -(j-m)^2 / (2 s^2) ), j = 0 .. N-1, j = 0 the oldest bar of the window

ALMA[t] = sum_j ( g[j] / sum_k g[k] ) * x[t-N+1+j]

The first output is at bar N-1.

Notes

• The peak is floored to a whole bar, as in the authors' code. At periods below about 5 this puts it on an older bar: at period 2 the line is almost entirely the previous bar.
• TA_MAType_ALMA runs this function at the default sigma and offset, so the line in MA and every function taking an MAType has the lag and noise stated above.
• The published paper's summary formula uses a different parameterisation; this is the form of the authors' own implementation.

Inputs

• inReal — Data on which to compute the average

Outputs

• outReal — Arnaud Legoux Moving Average line

Parameters

Parameter	Type	Default	Accepted values	Description
optInTimePeriod	integer	9	1–100000	Number of bars in the window
optInSigma	real	6	≥ 0.01	Divides the period to give the Gaussian's width in bars
optInOffset	real	0.85	0–1	Position of the peak weight, 0 at the oldest bar and 1 at the newest

Properties

Numerical Stability: Start-Independent

✅ Overlap Input i
☐ Independent Y-Axis
☐ Candlestick
☐ Display Shift

☐ Can Output NaN or ±Inf
✅ Identity at Period 1 i
✅ Uses Transcendental i
☐ Input Must Be Positive

Example

C

#include <stdio.h>
#include <ta_libc.h>

int n = 252;
double series[252]; /* your data, oldest first */
double out[252];
int outBegIdx, outNBElement;

TA_Initialize();
TA_ALMA( 0, n - 1, series, 9, 6.0, 0.85, &outBegIdx, &outNBElement, out );
printf( "%d values from bar %d; last out = %f\n", outNBElement, outBegIdx, out[outNBElement - 1] );

Rust

use ta_lib::Core;

let series = vec![0.0; 252]; // your data, oldest first
let mut out = vec![0.0; 252];

let core = Core::new();
let range = core.alma(0, series.len() - 1, &series, 9, 6.0, 0.85, &mut out)?;
println!("{} values from bar {}; last out = {}", range.count, range.beg_idx, out[range.count - 1]);

Java

import io.github.talib.Core;
import io.github.talib.OutRange;

double[] series = new double[252]; // your data, oldest first
double[] out = new double[252];

Core core = Core.DEFAULT;
OutRange r = core.alma(0, series.length - 1, series, 9, 6.0, 0.85, out);
System.out.println(r.count() + " values from bar " + r.begIdx() + "; last out = " + out[r.count() - 1]);

C#

using System;
using TALib;

var series = new double[252]; // your data, oldest first
var outReal = new double[252];

var core = Core.Default;
OutRange r = core.Alma(0, series.Length - 1, series, 9, 6.0, 0.85, outReal);
Console.WriteLine($"{r.Count} values from bar {r.BegIdx}; last outReal = {outReal[r.Count - 1]}");

TypeScript

import { alma } from 'ta-lib';

const series = new Float64Array(252); // your data, oldest first

const { begIdx, values } = alma(series, {
  timePeriod: 9,
  sigma: 6,
  offset: 0.85,
});
console.log(values.length + ' values from bar ' + begIdx + '; last values = ' + values[values.length - 1]);

Implementation

Added in 0.8.3 (ta-lib-python 0.8.3).

TA-Lib Definition: alma.c · alma.yaml

Native	File
C	ta_ALMA.c
Rust	alma.rs
Java	Core_ALMA.java
C#	Core_ALMA.cs
TypeScript	alma.ts

Python: talib.ALMA (ta-lib-python 0.8.3 or later), see ta-lib-python.

TA-Lib is also available for R and more using a wrapper.

See Also

WMA · SMA · TRIMA · HMA

References

• Arnaud Legoux and Dimitris Kouzis-Loukas, "ALMA; In search for the perfect Moving Average", November 2009. The authors' NinjaTrader implementation (2010) fixes the operational form above.