Median Absolute Deviation (MAD)

Robust dispersion estimator — the median of absolute deviations from the window's median. The median analogue of standard deviation: ignores extreme outliers (a single huge spike barely moves the result) and is widely used as a sturdier alternative to StdDev for risk reporting on heavy-tailed return distributions.

Quick reference

Item	Value
Family	Price Statistics
Input type	f64
Output type	f64
Output range	[0, ∞)
Default parameters	period required
Warmup period	period
Interpretation	Outlier-resistant volatility measure

Formula

med = median(window)
MAD = median( |x_i - med|  for x_i in window )

Multiplying MAD by 1.4826 gives a consistent estimator of the underlying Gaussian standard deviation ("robust σ"). Wickra returns raw MAD; multiply downstream if you want the σ equivalent. See crates/wickra-core/src/indicators/median_absolute_deviation.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 0	Rolling window.

Inputs / Outputs

Indicator<Input = f64, Output = f64>. Standard binding shapes.

Warmup

warmup_period() == period.

Edge cases

• All-identical input. MAD = 0.
• Outlier robustness. Single spike that would inflate StdDev by 5x barely changes MAD (~1x).
• Cost. Each update is O(period · log period) for the sort; acceptable for period ≤ 252.
• Reset. Clears the rolling window.

Examples

Rust

use wickra::{BatchExt, Indicator, MedianAbsoluteDeviation};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut series: Vec<f64> = (0..50).map(|i| 100.0 + f64::from(i % 5)).collect();
    series[25] = 200.0;  // outlier
    let mut mad = MedianAbsoluteDeviation::new(20)?;
    println!("row 30 MAD = {:?}", mad.batch(&series)[30]);
    Ok(())
}

Python

import numpy as np
import wickra as ta

series = (100 + np.arange(50) % 5).astype(float)
series[25] = 200.0
mad = ta.MedianAbsoluteDeviation(20)
print(mad.batch(series)[30])

Node

const wickra = require('wickra');
const mad = new wickra.MedianAbsoluteDeviation(20);
const series = Array.from({ length: 50 }, (_, i) => 100 + i % 5);
series[25] = 200;
console.log(mad.batch(series)[30]);

Streaming

use wickra::{Indicator, MedianAbsoluteDeviation};

let mut mad = MedianAbsoluteDeviation::new(50).unwrap();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(v) = mad.update(px) {
        let robust_sigma = v * 1.4826;
        // Use robust_sigma in place of StdDev for outlier-robust risk
    }
}

Interpretation

• Robust to outliers. MAD's breakdown point is 50% (you can corrupt half the data and MAD still works). StdDev's breakdown point is 0%.
• Use for heavy-tailed series. Financial returns are notoriously heavy-tailed; MAD-based risk gives more stable readings than StdDev-based.
• Robust σ. 1.4826 · MAD ≈ Gaussian σ for a normal population; useful when you want the σ-units interpretation but with outlier protection.

Common pitfalls

• MAD ≠ StdDev. Don't substitute MAD where σ is expected without applying the 1.4826 correction (or document the alternative units).
• Cost on large windows. O(period · log period). Long windows on minute bars can be slow.

References

• Frederick Hampel, The Influence Curve and Its Role in Robust Estimation, Journal of the American Statistical Association, 1974.

See also

• StdDev — non-robust cousin.
• Variance — squared cousin.
• CoefficientOfVariation — dispersion-normalised-by-mean.
• Indicators-Overview — full taxonomy.