Arnaud Legoux Moving Average: a Gaussian filter with an offset

What it measures

ALMA weights the lookback window with a Gaussian curve whose peak can be moved toward the recent end. Shifting the peak forward reduces lag; the Gaussian shape keeps the result smooth.

It is an attempt to get low lag without the overshoot that zero-lag constructions produce, and it largely succeeds — ALMA is noticeably smoother than a zero-lag EMA at similar responsiveness.

The two parameters do genuinely different things, which is unusual for a moving average and is why it is worth learning them.

How it is calculated

These are the steps Basis performs, verified against the published definition.

1. 1

   Build a Gaussian weight for each position in the lookback, centred at the offset position rather than the middle.

2. 2

   The sigma parameter controls how wide that Gaussian is — how much of the window contributes meaningfully.

3. 3

   Normalise the weights so they sum to one.

4. 4

   Take the weighted sum of prices across the window.

Settings

A window of nine with an offset of 0.85 and sigma of six is the common starting point. Raise sigma to widen the effective window and smooth further; lower the offset to trade responsiveness for stability. The two interact — a high offset with a low sigma concentrates almost all the weight on two or three bars, which is a very different thing from a moving average.

How to read it

• Read it as a moving average: slope for direction, crossings for changes, distance from price for extension.
• It sits closer to price than a simple average of the same period without the stair-stepping a very short average produces.
• Because it is a weighted window rather than a recursive filter, it has a hard memory — an old bar leaves the calculation entirely rather than decaying.
• That hard memory means a large old bar dropping out of the window moves the line with no new price action, which an exponential average never does.

Where it misleads

Related indicators