Detrended StdDev

Standard deviation of the OLS residuals over the rolling window. Detrends the input by fitting a linear regression, then measures the typical deviation from the fit. A pure "noise around the trend" measure, separating volatility from directional movement.

Quick reference

Item	Value
Family	Volatility & Bands
Input type	f64
Output type	f64
Output range	[0, ∞)
Default parameters	period required
Warmup period	period
Interpretation	Residual-only volatility; trending markets have low DetrendedStdDev

Formula

1. Fit OLS line y = a + b·x over the rolling window
2. residual_i = y_i - (a + b·x_i)
3. DetrendedStdDev = √( (1/n) · Σ residual² )

Mathematically equivalent to StandardError using a different denominator. See crates/wickra-core/src/indicators/detrended_stddev.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 2	Rolling window.

Inputs / Outputs

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

Warmup

warmup_period() == period.

Edge cases

• Perfect linear fit. Residuals all zero → output 0.0.
• Pure noise. Output approximates the same as plain StdDev (no trend to remove).
• Reset. Clears running sums.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let series: Vec<f64> = (0..50)
        .map(|i| f64::from(i) * 0.5 + (f64::from(i) * 0.3).sin())
        .collect();
    let mut d = DetrendedStdDev::new(20)?;
    println!("row 30 = {:?}", d.batch(&series)[30]);
    // Much lower than plain StdDev which includes the trend
    Ok(())
}

Python

import numpy as np
import wickra as ta

series = np.arange(50, dtype=float) * 0.5 + np.sin(np.linspace(0, 15, 50))
d = ta.DetrendedStdDev(20)
print(d.batch(series)[30])

Node

const wickra = require('wickra');
const d = new wickra.DetrendedStdDev(20);
const series = Array.from({ length: 50 }, (_, i) => i * 0.5 + Math.sin(i * 0.3));
console.log(d.batch(series)[30]);

Streaming

use wickra::{DetrendedStdDev, Indicator};

let mut d = DetrendedStdDev::new(20).unwrap();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(v) = d.update(px) {
        // v is pure noise around the trend
    }
}

Interpretation

• Vs plain StdDev. On the same window, plain StdDev includes the trend's contribution to variance; DetrendedStdDev removes it. A trending series can have high StdDev and low DetrendedStdDev — meaning the trend is real, not noise.
• Volatility-of-residuals. Use to size noise-based stops: a Bollinger-style band of ±2 · DetrendedStdDev around the regression line catches mean-reverting moves while ignoring the trend.
• Regime classifier. Low DetrendedStdDev with high R² = clean trend; high DetrendedStdDev = noisy regime.

Common pitfalls

• Confused with StdDev. Different units of measurement; not interchangeable. Detrended is always ≤ StdDev for the same window.
• Period choice. Same as StdDev — short windows are noisy.

References

• Standard regression-residual statistic; documented in any statistics text.

See also

• StandardError — close cousin (uses n - 2 denominator).
• StdDev — non-detrended baseline.
• Variance — squared cousin.
• LinearRegression — the fit being used.
• Indicators-Overview — full taxonomy.