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.

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
☐ Can Output NaN or ±Inf
✅ Identity at Period 1 i

Implementation

TA-Lib Definition: alma.c · alma.yaml

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

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

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.