LinRegChannel

Rolling linear-regression line wrapped by ±k·σ of the residuals. Where Bollinger measures dispersion about the mean, the LinReg Channel measures it about the trend.

Quick reference

Field	Value
Family	Bands & Channels
Input type	f64 (typically the close price)
Output type	LinRegChannelOutput { upper, middle, lower }
Output range	unbounded; lower ≤ middle ≤ upper
Default parameters	period = 20, multiplier = 2.0
Warmup period	period (exact)
Interpretation	Channel breakouts are statistically meaningful in the direction of trend, not just in absolute price.

Formula

fit y = a + b·x by OLS over the last `period` closes (x = 0..period − 1)
residual_i = y_i − (a + b · x_i)
sigma      = sqrt( Σ residual_i² / period )      // population stddev
middle     = a + b · (period − 1)                // endpoint of the line
upper      = middle + multiplier · sigma
lower      = middle − multiplier · sigma

A perfectly linear input has zero residuals, so the channel collapses onto the regression line — a useful sanity check. The slope/intercept are fitted by ordinary least squares over the live window each bar (O(period) per update; see the note in linreg_channel.rs:108).

Parameters

Name	Type	Default	Constraint	Source
period	usize	20	>= 2	LinRegChannel::new (linreg_channel.rs:66)
multiplier	f64	2.0	finite, > 0	linreg_channel.rs:72

period < 2 returns [Error::InvalidPeriod] (a regression line is undefined for a single point); 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, LinRegChannel, LinRegChannelOutput};
// LinRegChannel: Input = f64, Output = LinRegChannelOutput
const _: fn(&mut LinRegChannel, f64) -> Option<LinRegChannelOutput> = <LinRegChannel as Indicator>::update;

• Python streaming. update(value) returns (upper, middle, lower) or None.
• Python batch. LinRegChannel.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.

Warmup

warmup_period() returns period. The window must hold a full period values before the OLS fit and residual stddev are defined, so the first non-None output lands on input period (index period − 1). Readiness is window.len() == period.

Edge cases

• Perfectly linear input. Zero residuals ⇒ sigma = 0 ⇒ upper == middle == lower (test perfect_line_collapses_channel).
• Constant series. A flat line is a degenerate trend; the channel collapses onto the constant (test constant_series_collapses_channel).
• Ordering. upper >= middle >= lower always holds (sigma >= 0).
• Reset. reset() clears the window and restarts warmup.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // period 3 over [1, 2, 9]: fitted line y = 4·x, endpoint 8;
    // residuals 1, −2, 1 → population sigma = sqrt(2).
    let mut lc = LinRegChannel::new(3, 2.0)?;
    if let Some(o) = lc.batch(&[1.0, 2.0, 9.0]).into_iter().flatten().last() {
        println!("middle={:.4} upper={:.4} lower={:.4}", o.middle, o.upper, o.lower);
    }
    Ok(())
}

Output:

middle=8.0000 upper=10.8284 lower=5.1716

upper = 8 + 2·sqrt(2) ≈ 10.8284, lower = 8 − 2·sqrt(2) ≈ 5.1716 (test reference_values).

Python

import numpy as np
import wickra as ta

lc = ta.LinRegChannel(3, 2.0)
print(lc.batch(np.array([1.0, 2.0, 9.0]))[-1])  # [10.8284  8.  5.1716]

Node

const ta = require('wickra');
const lc = new ta.LinRegChannel(3, 2.0);
lc.update(1); lc.update(2);
console.log(lc.update(9)); // { upper: ~10.83, middle: 8, lower: ~5.17 }

Interpretation

The LinReg Channel detrends its dispersion measure, so a steady drift does not inflate the band width the way a sigma-about-the-mean band would:

1. Trend channel. The midline is the regression endpoint — a least-squares estimate of "fair value" given the recent slope. Closes beyond the bands are excursions relative to the fitted trend, not the flat mean.
2. Breakout quality. Because the bands hug the trend, a close outside the upper band in an uptrend is a genuine acceleration, whereas a mean-based band would already be wide and miss it.

Common pitfalls

• Expecting Bollinger-like width in a trend. A strongly trending series has small residuals about its regression line, so this channel is much narrower than BollingerBands on the same data.
• Reusing period < 2. The constructor rejects it — there is no line through one point.

References

• TA-Lib's LINEARREG family for the rolling-OLS endpoint.
• John Bollinger's Bollinger on Bollinger Bands (2001) for the parallel to the σ-based envelope this channel detrends.

See also

• StandardErrorBands — same skeleton but uses the n − 2 OLS standard error instead of the population stddev.
• LinearRegression — the bare endpoint.
• LinRegSlope — the slope component.
• BollingerBands — dispersion about the mean.