MESA Adaptive Moving Average (MAMA)

Summary

MESA Adaptive Moving Average: an adaptive EMA whose smoothing factor is driven by the dominant-cycle phase rate measured with a Hilbert transform. Emits two lines, MAMA and its slower follower FAMA. MAMA crossing above FAMA is bullish; crossing below is bearish.

Chart

Reference data (CSV) · Chart (SVG)

Chart metadata i

Outputs

• outMAMA: line
• outFAMA: dash_line

Formula

phase = atan(Q1/I1) in degrees; deltaPhase = max(1, prevPhase - phase) alpha = max(fastLimit/deltaPhase, slowLimit) if deltaPhase>1 else fastLimit MAMA = alpha*price + (1-alpha)*MAMA_prev FAMA = (alpha/2)*MAMA + (1-alpha/2)*FAMA_prev

Inputs

• inReal — Price series to smooth

Outputs

• outMAMA — Adaptive moving average (fast line)
• outFAMA — Following adaptive moving average, using half the alpha (slow line)

Parameters

Parameter	Type	Default	Accepted values	Description
optInFastLimit	real	0.5	0.01–0.99	Upper bound on the adaptive smoothing factor
optInSlowLimit	real	0.05	0.01–0.99	Lower bound on the adaptive smoothing factor

Properties

Numerical Stability: Initial Unstable Period

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

☐ Can Output NaN or ±Inf
☐ Identity at Period 1
✅ 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 mama[252], fama[252];
int outBegIdx, outNBElement;

TA_Initialize();
TA_MAMA( 0, n - 1, series, 0.5, 0.05, &outBegIdx, &outNBElement, mama, fama );
printf( "%d values from bar %d; last mama = %f\n", outNBElement, outBegIdx, mama[outNBElement - 1] );

Rust

use ta_lib::Core;

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

let core = Core::new();
let range = core.mama(0, series.len() - 1, &series, 0.5, 0.05, &mut mama, &mut fama)?;
println!("{} values from bar {}; last mama = {}", range.count, range.beg_idx, mama[range.count - 1]);

Java

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

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

Core core = Core.DEFAULT;
OutRange r = core.mama(0, series.length - 1, series, 0.5, 0.05, mama, fama);
System.out.println(r.count() + " values from bar " + r.begIdx() + "; last mama = " + mama[r.count() - 1]);

C#

using System;
using TALib;

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

var core = Core.Default;
OutRange r = core.Mama(0, series.Length - 1, series, 0.5, 0.05, mama, fama);
Console.WriteLine($"{r.Count} values from bar {r.BegIdx}; last mama = {mama[r.Count - 1]}");

TypeScript

import { mama } from 'ta-lib';

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

const { begIdx, outMama, outFama } = mama(series, {
  fastLimit: 0.5,
  slowLimit: 0.05,
});
console.log(outMama.length + ' values from bar ' + begIdx + '; last outMama = ' + outMama[outMama.length - 1]);

Implementation

Added in 0.4.0.

TA-Lib Definition: mama.c · mama.yaml

Native	File
C	ta_MAMA.c
Rust	mama.rs
Java	Core_MAMA.java
C#	Core_MAMA.cs
TypeScript	mama.ts

Python: talib.MAMA, see ta-lib-python.

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

Aliases

MESA Adaptive Moving Average, Ehlers MAMA

See Also

MA · WMA · HT_DCPERIOD

References

• John F. Ehlers, Rocket Science for Traders: Digital Signal Processing Applications, John Wiley & Sons (ISBN 0471405671)