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MESA Adaptive Moving Average

Ehlers DSP moving-average adaptive ehlers dsp trend

MAMA adapts to price movement in an entirely new and unique way based on the rate change of phase.

Visual Example

MESA Adaptive Moving Average — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-06-25 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

The MESA Adaptive Moving Average indicator is a technical analysis tool that mama adapts to price movement in an entirely new and unique way based on the rate change of phase.

This indicator is primarily used for identifying key market conditions. It provides a robust signal that can be easily integrated into both simple strategies and more complex machine learning feature pipelines. Compared to its alternatives, it offers a distinct balance of responsiveness and stability.

Traders often combine this with other metrics to confirm signals and avoid false positives during sideways market regimes. It remains a standard tool for systematic trading models.

Use as an adaptive trend filter that automatically speeds up in fast markets and slows in choppy ones. The FAMA line crossing MAMA provides high-probability trend change signals.

Presented in Rocket Science for Traders (2001), MAMA adapts its alpha based on the rate of phase change measured by the Hilbert Transform Discriminator. Fast cycles produce large alpha for responsiveness; slow cycles produce small alpha to reduce noise.

QuantWave implements this indicator via the universal Next<T> trait, guaranteeing bit-identical results between Rust streaming, Python streaming, and Polars batch (.ta() / map_batches) surfaces.

Formula / Specification

Implementation (quantwave-core/src/indicators/mama.rs):

[ \text{MAMA} = \alpha \cdot \text{Price} + (1 - \alpha) \cdot \text{MAMA}{1} ] [ \text{FAMA} = 0.5\alpha \cdot \text{MAMA} + (1 - 0.5\alpha) \cdot \text{FAMA} ]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/mama.json.

Parameters

Parameter Default Description
fast_limit 0.5 Fast limit for alpha
slow_limit 0.05 Slow limit for alpha

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::MAMA;
use quantwave_core::traits::Next;

let mut ind = MAMA::new(0.5);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import MAMA

ind = MAMA(0.5)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_mesa_adaptive_moving_average(series: pl.Series) -> pl.Series:
    ind = qw.MAMA(0.5)
    return pl.Series([ind.next(float(v)) for v in series.to_list()])

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").map_batches(apply_mesa_adaptive_moving_average, return_dtype=pl.Float64).alias("mesa_adaptive_moving_average")
    )
    .collect()
)

All surfaces are bit-identical via the single Next<T> implementation and proptests.

Edge Cases & Limitations

  • Recursive DSP filters require a warm-up period; first N bars may be unstable or raw-pass-through.
  • Designed for cyclic/mean-reverting regimes; trending markets can produce lag or drift.
  • Parameter period (or equivalent) controls cutoff — too small adds noise, too large adds lag.
  • Prefer chaining with other Ehlers tools (Roofing Filter, SuperSmoother) on noisy inputs.
  • Validated via proptests against gold-standard vectors where available.
  • No look-ahead bias; suitable for live streaming and batch feature pipelines.

Boundary Behavior

Condition Behavior
Warm-up Leading bars return NaN until warmup_bars is satisfied.
period > len When period exceeds series length, output is all NaN.
NaN inputs NaN in input propagates to output (NaN out).
Invalid params Non-positive period or missing required params raise ValueError.
Empty data Empty input returns an empty result series.

Sources & References

Primary Source: https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/implemented/MAMA.pdf

Implementation: quantwave-core/src/indicators/mama.rs (MAMA / MAMA_METADATA). Parity: quantwave-core/tests/gold_standard/mama.json

Provenance: Standards bulk upgrade 2026-06-25 IST — see docs/DOCUMENTATION_STANDARDS.md.