MedianChannel

A robust analogue of Bollinger Bands: centre on the rolling median, size by the median absolute deviation (MAD). 50% breakdown point — outliers barely move it.

Quick reference

Field	Value
Family	Bands & Channels
Input type	f64
Output type	MedianChannelOutput { upper, middle, lower }
Output range	unbounded; lower ≤ middle ≤ upper
Default parameters	period = 20, multiplier = 2.0
Warmup period	period (exact — first emission on bar period)
Interpretation	Robust Bollinger: median centreline, MAD-scaled width — unmoved by spikes and gaps.

Formula

middle = median(close, period)
MAD    = median( | close_i − middle | )
upper  = middle + multiplier · MAD
lower  = middle − multiplier · MAD

Where BollingerBands centre on the mean and scale by the standard deviation — both of which a single spike can drag arbitrarily far — the Median Channel uses two order statistics. The breakdown point of the median and MAD is 50%: up to half the window can be contaminated before the centre or width is materially distorted. Both quantiles use the type-7 interpolation shared with RollingQuantile. Source: crates/wickra-core/src/indicators/median_channel.rs.

Parameters

Name	Type	Default	Constraint	Source
period	usize	20	>= 1	MedianChannel::new (median_channel.rs:67)
multiplier	f64	2.0	finite, > 0	median_channel.rs:67

period == 0 returns [Error::PeriodZero]; a non-finite or non-positive multiplier returns [Error::NonPositiveMultiplier]. Python defaults come from #[pyo3(signature = (period=20, multiplier=2.0))]; the Node constructor takes both arguments explicitly.

Inputs / Outputs

use wickra::{Indicator, MedianChannel, MedianChannelOutput};
// MedianChannel: Input = f64, Output = MedianChannelOutput
const _: fn(&mut MedianChannel, f64) -> Option<MedianChannelOutput> =
    <MedianChannel as Indicator>::update;

• Python streaming. update(value) returns (upper, middle, lower) or None.
• Python batch. MedianChannel.batch(prices) returns an (n, 3)np.ndarray with columns [upper, middle, lower]; warmup rows are NaN.
• Node streaming. update(value) returns a { upper, middle, lower } object or null.
• Node batch. batch(prices) returns a flat Array<number> of length n * 3 interleaved per row [u0, m0, l0, …].

Warmup

warmup_period() reports period and is exact: both the median and the MAD need a full window, so the first non-None output lands on bar period. Pinned by warms_up_then_emits (four Nones then Some for period = 5).

Edge cases

• Outlier robustness. A single huge spike leaves the median centre unchanged; pinned by robust_to_outlier (window [1,2,3,4,1000] → median 3).
• Flat / low-dispersion window. When more than half the window shares the median value MAD = 0, collapsing the channel to upper == middle == lower.
• Ordering. upper ≥ middle ≥ lower always holds because MAD ≥ 0 and multiplier > 0.
• Reset. reset() clears the window and both scratch buffers; the next update restarts warmup (test reset_clears_state).

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut mc = MedianChannel::new(5, 2.0)?;
    for v in mc.batch(&[1.0, 2.0, 3.0, 4.0, 5.0]) {
        println!("{:?}", v);
    }
    Ok(())
}

Output:

None
None
None
None
Some(MedianChannelOutput { upper: 5.0, middle: 3.0, lower: 1.0 })

For [1,2,3,4,5] the median is 3; the absolute deviations sorted are [0,1,1,2,2] so MAD = 1; with multiplier = 2 the bands sit at 3 ± 2. This matches the known_channel test.

Python

import numpy as np
import wickra as ta

mc = ta.MedianChannel(5, 2.0)
print(mc.batch(np.array([1.0, 2.0, 3.0, 4.0, 5.0])))

Output:

[[nan nan nan]
 [nan nan nan]
 [nan nan nan]
 [nan nan nan]
 [ 5.  3.  1.]]

Node

const ta = require('wickra');
const mc = new ta.MedianChannel(5, 2.0);
for (const v of [1, 2, 3, 4]) mc.update(v);
console.log(mc.update(5)); // { upper: 5, middle: 3, lower: 1 }

Interpretation

The Median Channel is the tool to reach for when the data is too noisy for Bollinger Bands:

1. Robust mean reversion. The median centreline is unmoved by gaps and flash spikes, so band tags reflect genuine excursions rather than one bad print dragging the mean.
2. Stable width. MAD ignores the magnitude of outliers beyond their rank, so the channel does not flare after a single large bar the way a sigma-scaled band does.

Common pitfalls

• Treating multiplier as a sigma count. It scales the MAD, not the standard deviation; for normal data MAD ≈ 0.674σ, so a multiplier of 2 here is roughly a 1.35σ Bollinger band, not 2σ.
• Very short windows. With a small period the MAD is computed from few deviations and can be 0 whenever the median value repeats; use period ≥ 10 for a stable width.

References

• Rousseeuw, P. J., & Croux, C., "Alternatives to the Median Absolute Deviation," Journal of the American Statistical Association, 1993.

See also

• BollingerBands — mean ± sigma (non-robust) envelope.
• QuartileBands — non-parametric quartile envelope.
• RollingQuantile — the shared type-7 quantile engine.
• MedianAbsoluteDeviation — the MAD statistic on its own.