StandardErrorBands

Linear-regression line wrapped by the OLS standard error (n − 2 denominator). Statistically-correct prediction-interval bands; slightly wider than LinRegChannel.

Quick reference

Field	Value
Family	Bands & Channels
Input type	f64 (typically the close price)
Output type	StandardErrorBandsOutput { upper, middle, lower }
Output range	unbounded; lower ≤ middle ≤ upper
Default parameters	period = 21, multiplier = 2.0
Warmup period	period (exact)
Interpretation	Bands describe a prediction interval around the regression line. Closes outside are statistically unusual.

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)
stderr     = sqrt( Σ residual_i² / (period − 2) )   // OLS standard error
middle     = a + b · (period − 1)
upper      = middle + multiplier · stderr
lower      = middle − multiplier · stderr

The n − 2 divisor (two degrees of freedom consumed by the slope and intercept) gives a slightly wider channel than the population stddev used by LinRegChannel — exactly by a factor sqrt(n / (n − 2)) (≈ 1.054 at n = 20).

Jon Andersen's original publication pairs the bands with a default multiplier = 2.0 and a 3-bar SMA smoothing of all three outputs; Wickra reports the raw bands so callers can pipe them through their own smoother (e.g. Sma::new(3)).

Parameters

Name	Type	Default	Constraint	Source
period	usize	21	>= 3	StandardErrorBands::new (standard_error_bands.rs:74)
multiplier	f64	2.0	finite, > 0	standard_error_bands.rs:80

period < 3 returns [Error::InvalidPeriod] (the n − 2 denominator needs at least 3 points); a non-finite or non-positive multiplier returns [Error::NonPositiveMultiplier]. Python defaults come from #[pyo3(signature = (period=21, multiplier=2.0))]; the Node constructor takes both arguments explicitly.

Inputs / Outputs

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

• Python streaming. update(value) returns (upper, middle, lower) or None.
• Python batch. StandardErrorBands.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 standard error 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 ⇒ stderr = 0 ⇒ upper == middle == lower (test perfect_line_collapses_bands).
• Wider than the population band. On identical residuals the n − 2 standard error strictly exceeds the population stddev by sqrt(n/(n−2)) (test standard_error_exceeds_population_stddev).
• Ordering. upper >= middle >= lower always holds.
• Reset. reset() clears the window and restarts warmup.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    // period 3 over [1, 2, 9]: endpoint 8, SSE = 6, n − 2 = 1 → stderr = sqrt(6).
    let mut seb = StandardErrorBands::new(3, 2.0)?;
    if let Some(o) = seb.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=12.8990 lower=3.1010

upper = 8 + 2·sqrt(6) ≈ 12.8990, lower = 8 − 2·sqrt(6) ≈ 3.1010 (test reference_values).

Python

import numpy as np
import wickra as ta

seb = ta.StandardErrorBands(3, 2.0)
print(seb.batch(np.array([1.0, 2.0, 9.0]))[-1])  # [12.899  8.  3.101]

Node

const ta = require('wickra');
const seb = new ta.StandardErrorBands(3, 2.0);
seb.update(1); seb.update(2);
console.log(seb.update(9)); // { upper: ~12.90, middle: 8, lower: ~3.10 }

Interpretation

Standard Error Bands describe a prediction interval around the regression endpoint: at multiplier = 2.0 the bands approximate a 95 % interval for a new observation given the recent trend (the normal-theory reading). Practical use mirrors LinRegChannel:

1. Channel width as trend strength. A tight band means the recent data hugs its regression line — a clean trend. A flaring band means the fit is poor — choppy, trendless action.
2. Reversion vs continuation. Closes outside the band are statistically unusual relative to the trend and often revert; sustained closes outside warn the trend's slope is changing.

Common pitfalls

• Comparing band width to LinRegChannel one-for-one. Standard Error Bands are always wider by sqrt(n/(n−2)) on the same data; do not read the difference as a regime change.
• Using period < 3. The n − 2 denominator is undefined; the constructor rejects it.

References

• Jon Andersen, Standard Error Bands, Technical Analysis of Stocks & Commodities, September 1996.

See also

• LinRegChannel — population-stddev variant.
• LinearRegression — the bare endpoint.
• BollingerBands — sigma about the mean (not the trend).