MESA Adaptive Moving Average (MAMA and FAMA) explained

The MESA Adaptive Moving Average, MAMA for short, is a moving average that changes its speed according to how fast the market's dominant price cycle is moving. John Ehlers, an engineer who spent his early career in signal processing, published it in September 2001. It comes with a companion line, the Following Adaptive Moving Average (FAMA), and the two are read together, much like a MACD line and its signal.

MAMA behaves unlike any other average in Finabase. Instead of gliding smoothly, it holds nearly still for days and then jumps a large part of the way toward price in a single bar. This guide explains, without the heavy math, what drives that behaviour, shows the exact update rule recovered from Finabase's own Amazon data, and covers how to read MAMA/FAMA crossovers and where they fail.

The idea: speed up when the cycle turns

Ehlers models price as a trend plus cycles. His MESA (maximum entropy spectral analysis) and Hilbert-transform tools estimate the phase of the dominant cycle on every bar: where in its up-and-down rhythm the market currently is, measured as an angle.

When the market is in a steady cycle, the phase advances by a small, regular amount each bar. When something changes, a breakout or a reversal, the measured phase jumps. MAMA uses that jump as its speed control:

• Phase changing slowly: the market is following its rhythm, so smooth heavily (α near the slow limit).
• Phase changing fast: something is happening, so catch up quickly (α near the fast limit).

You do not need to compute the Hilbert transform to use MAMA. You need to understand that its α is driven by the rate of phase change, and that this produces a step-like line.

The formula

Because the phase is measured in degrees and normally advances by many degrees per bar, the ratio fast limit ÷ ΔPhase is usually tiny and gets clamped to the slow limit. When the phase barely advances or even moves backwards (a reset), ΔPhase hits its 1-degree floor and α jumps to the fast limit. That is why α tends to sit at one of the two extremes.

A worked example on Amazon: recovering α from the chart

You can recover α for any day from Finabase's MAMA line, because the update is an EMA: α = (MAMA today − MAMA yesterday) ÷ (close today − MAMA yesterday). Here is Amazon (AMZN) in early April 2026.

Check April 9 by hand. With α = 0.5, MAMA = 0.5 × 233.65 + 0.5 × 211.70 = $222.68, and FAMA = 0.25 × 222.68 + 0.75 × 211.36 = $214.19. Both match the chart.

On April 8 Amazon rose $7.48, but α was at the slow limit and MAMA moved only 50 cents. On April 9, with another big gain, the phase reset, α hit 0.5, and MAMA closed half the gap in one bar, rising $10.98. The next day it was back to crawling.

Reading MAMA and FAMA on a real chart

The staircase shape is visible throughout Amazon's year. MAMA (the faster line) holds flat, then steps; FAMA follows more smoothly behind it.

Crossovers. MAMA crossing above FAMA is read as bullish; below, bearish. Because FAMA trails MAMA by design, crossings are infrequent: over the year Amazon had 13. Several were well timed. The cross up on April 8, 2026 at a close of $221.25 came after the February low of $196.00 and was followed by a 24.3% gain over the next 20 sessions. The cross down on June 2 at $256.52 was followed by a 5.8% decline over 20 sessions.

Others were not. A cross down on July 24 at $232.11 came right before a sharp rally: Amazon was 18.3% higher ten sessions later. And in October the lines crossed four times in 13 sessions as price chopped between $249 and $263.

How traders use MAMA

MAMA/FAMA crossovers as a trend signal. This is Ehlers' own use. The two lines are designed to cross only when the cycle measurement says the market has genuinely shifted, so there are far fewer crossings than with two ordinary averages.

As a trailing reference. Because MAMA steps toward price on significant moves and then holds, some traders use it like a ratcheting stop: it rarely gives back ground in a strong trend.

Tuning the limits. A higher fast limit makes the jumps larger; a higher slow limit makes the line drift more between jumps. Ehlers' defaults, 0.5 and 0.05, suit daily data for most liquid instruments.

Pitfalls and limitations

It assumes cycles. The phase measurement is meaningful when a market has a measurable dominant cycle. In a strong, cycle-free trend or around news gaps, the phase readings can be erratic and MAMA's jumps can fire at odd times.

Steps can look like signals. A sudden MAMA jump is not by itself a buy or sell signal; it is the indicator catching up. Read crossings with FAMA, not individual steps.

Opaque mechanics. Few users can verify the Hilbert-transform internals. That is not a reason to avoid MAMA, but it is a reason to test it on your own symbols rather than trusting its reputation.

Comparison table

For the fixed baseline see Exponential moving average (EMA): formula and how to use it.

How Finabase calculates and scores MAMA

Finabase computes MAMA and FAMA with TA-Lib's MAMA function on closing prices. The study, listed as "MESA Adaptive Moving Average," defaults to a fast limit of 0.5 and a slow limit of 0.05, and draws both lines on the price chart.

In the technical gauge, MAMA is one overlay row, decided by the MAMA line: a close at or above it counts as Bullish, below it as Bearish. The Scanner tracks both lines at the default limits and lists stocks whose close crossed either MAMA or FAMA, with the date. Neither the gauge nor the Scanner scores the MAMA/FAMA crossover itself; you read that from the chart.

Frequently asked questions

What is the difference between MAMA and FAMA?

MAMA is the adaptive average itself. FAMA is a slower follower that averages MAMA with half of MAMA's α. Their crossings are the standard signal.

What do the fast limit and slow limit mean?

They are the largest and smallest smoothing constants MAMA can use. With 0.5 and 0.05, MAMA moves between half and one-twentieth of the gap to price each bar, depending on the cycle phase.

Why does MAMA move in steps?

Because the measured phase usually advances enough to clamp α at the slow limit, and only on phase-reset bars does α jump to the fast limit. On Amazon's daily chart, about two-thirds of days were at the slow limit and most of the rest at the fast one.

Summary

MAMA is an exponential average whose speed is set each bar by the rate at which the market's cycle phase is changing. That makes it crawl most of the time and jump on significant bars, as Amazon's $10.98 step on April 9, 2026 showed. Its companion FAMA follows at half speed, and their crossovers are the signal, infrequent and sometimes very well timed, sometimes not. Use it as one view of trend among several, and test it on the markets you trade.