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Fractal Adaptive Moving Average

Ehlers DSP moving-average adaptive fractal smoothing

An adaptive moving average that uses the fractal dimension of prices to dynamically change its smoothing constant.

Visual Example

Fractal Adaptive Moving Average — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-07-01 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

An adaptive moving average that uses the fractal dimension of prices to dynamically change its smoothing constant.

Use as an adaptive moving average that slows dramatically during consolidation and speeds up during trending phases. Outperforms fixed-period MAs in ranging markets by avoiding false crossovers.

Part of QuantWave's Ehlers digital signal processing suite. Designed for low-lag cycle and trend work — pair with Roofing Filter or SuperSmoother on noisy inputs.

The Fractal Adaptive Moving Average uses the fractal dimension of recent price action to adapt its smoothing constant. During trending markets the fractal dimension approaches 1 (a line) producing a fast-reacting EMA; during ranging markets the dimension approaches 2 (a plane) slowing the average dramatically to filter chop.

Typical applications:

  • Use for cycle timing in mean-reverting regimes
  • Gate with Hurst exponent or ADX before taking cycle signals
  • Allow 16+ bars warm-up for filter state to stabilise
  • Chain with Roofing Filter when input is noisy

QuantWave implements this via the universal Next<T> trait — bit-identical across Rust streaming, Python streaming, and Polars .ta() batch plugins.

Formula / Specification

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

[ D = \frac{\log(N_1 + N_2) - \log(N_3)}{\log(2)} ] [ \alpha = \exp(-4.6 (D - 1)) ] [ \text{FRAMA}t = \alpha P_t + (1 - \alpha) \text{FRAMA} ]

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

Parameters

Parameter Default Description
length 16 Length (must be an even number; odd values will be incremented by 1).

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::FRAMA;
use quantwave_core::traits::Next;

let mut ind = FRAMA::new(16);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import FRAMA

ind = FRAMA(16)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_fractal_adaptive_moving_average(series: pl.Series) -> pl.Series:
    ind = qw.FRAMA(16)
    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_fractal_adaptive_moving_average, return_dtype=pl.Float64).alias("fractal_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/FRAMA.pdf

Implementation: quantwave-core/src/indicators/frama.rs (FRAMA / FRAMA_METADATA). Parity: quantwave-core/tests/gold_standard/frama.json

Provenance: Standards bulk upgrade 2026-07-01 IST — see docs/DOCUMENTATION_STANDARDS.md.