Standard Error

Standard error of the rolling OLS regression line. Measures the typical deviation of input values from the fitted trend line — a residual-based volatility measure that filters out the trend component first.

Quick reference

Item	Value
Family	Price Statistics
Input type	f64
Output type	f64
Output range	[0, ∞)
Default parameters	period required
Warmup period	period
Interpretation	Trend-detrended typical deviation

Formula

slope    = (n·Σxy - Σx·Σy) / (n·Σxx - (Σx)²)
SS_total = Σy² - n·ȳ²
RSS      = SS_total - slope² · S_xx     (residual sum of squares)
StdErr   = √(RSS / (n - 2))             (n - 2 residual d.o.f.)

where S_xx = (n·Σxx - (Σx)²) / n. See crates/wickra-core/src/indicators/standard_error.rs.

Parameters

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

Inputs / Outputs

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

Warmup

warmup_period() == period.

Edge cases

• Perfect fit. RSS = 0 → StdErr = 0.
• Flat input. SS_total = 0 → StdErr = 0.
• Constant input. Same as flat.
• Reset. Clears running sums.

Examples

Rust

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

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 se = StandardError::new(20)?;
    println!("row 30 = {:?}", se.batch(&series)[30]);
    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))
se = ta.StandardError(20)
print(se.batch(series)[30])

Node

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

Streaming

use wickra::{Indicator, StandardError};

let mut se = StandardError::new(20).unwrap();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(v) = se.update(px) {
        // v is the trend-detrended volatility
    }
}

Interpretation

• Trend-detrended volatility. Unlike StdDev, StandardError removes the linear trend component first. Useful when you want to measure "noise around the trend" rather than "noise + trend".
• Standard Error Bands. Stack ±2 · StandardError around the fitted linear regression line to form regression-residual bands — see StandardErrorBands.
• Vs StdDev. Same data with strong trend: StdDev high (driven by trend), StandardError low (residual after detrending).

Common pitfalls

• Period interpretation. The period argument here is the number of bars in the regression window, not the order of polynomial fit (which is fixed at linear).
• Cost. Running sums make each update O(1) — well-suited for streaming.

References

• Standard regression statistic; documented in any statistics text.

See also

• StandardErrorBands — band visualisation.
• LinearRegression — the line itself.
• LinRegSlope — slope alone.
• RSquared — explained-variance ratio.
• Indicators-Overview — full taxonomy.