MAD

Ehlers DSP volatility statistics robust ehlers

Moving Average Difference: 100 * (SMA(short) - SMA(long)) / SMA(long)

Visual Example

MAD — 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 MAD indicator is a technical analysis tool that moving average difference: 100 * (sma(short) - sma(long)) / sma(long)

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 a robust volatility measure when outliers or fat-tailed distributions would distort standard deviation. Works well for position sizing and volatility-based stop placement.

Mean Absolute Deviation measures dispersion as the average absolute difference from the median rather than the squared difference from the mean used by standard deviation. It is less sensitive to outliers, making it a more robust volatility estimate for financial time series with fat tails.

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/mad.rs):

\[ MAD = 100 \times \frac{SMA(short) - SMA(long)}{SMA(long)} \]

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

Parameters

Parameter	Default	Description
`short_period`	8	Short-term SMA period
`long_period`	23	Long-term SMA period

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::MAD;
use quantwave_core::traits::Next;

let mut ind = MAD::new(8);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import MAD

ind = MAD(8)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_mad(series: pl.Series) -> pl.Series:
    ind = qw.MAD(8)
    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_mad, return_dtype=pl.Float64).alias("mad")
    )
    .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/traderstipsreference/TRADERS’ TIPS - OCTOBER 2021.html

Implementation: quantwave-core/src/indicators/mad.rs (MAD / MAD_METADATA). Parity: quantwave-core/tests/gold_standard/mad.json

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

MAD