Variance

Rolling population variance of the input series. The second central moment of the rolling distribution — the squared sibling of StdDev. Natural input to risk calculations that expect squared returns (portfolio variance, covariance matrices).

Quick reference

Item	Value
Family	Price Statistics
Input type	f64
Output type	f64
Output range	[0, ∞)
Default parameters	period required
Warmup period	period
Interpretation	Squared dispersion; use StdDev for human-readable units

Formula

mean     = (1/n) · Σ price
Variance = (1/n) · Σ price² - mean²

Population variance (denominator n), not sample variance. See crates/wickra-core/src/indicators/variance.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 0	Rolling window.

Inputs / Outputs

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

Warmup

warmup_period() == period.

Edge cases

• Constant input. Variance = 0.
• Catastrophic cancellation. Wickra uses Welford's online formula plus periodic reseeding to keep f64 precision stable on long-running streams.
• Reset. Clears the rolling buffer and sums.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let prices: Vec<f64> = (0..50)
        .map(|i| 100.0 + (f64::from(i) * 0.3).sin() * 5.0)
        .collect();
    let mut v = Variance::new(20)?;
    println!("row 30 = {:?}", v.batch(&prices)[30]);
    Ok(())
}

Python

import numpy as np
import wickra as ta

prices = 100 + np.sin(np.linspace(0, 15, 50)) * 5
v = ta.Variance(20)
print(v.batch(prices)[30])

Node

const wickra = require('wickra');
const v = new wickra.Variance(20);
const prices = Array.from({ length: 50 }, (_, i) => 100 + Math.sin(i * 0.3) * 5);
console.log(v.batch(prices)[30]);

Streaming

use wickra::{Indicator, Variance};

let mut v = Variance::new(252).unwrap();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(val) = v.update(px) {
        // val is rolling variance in squared price units
    }
}

Interpretation

Variance is the second central moment. For human-readable units, use StdDev instead — it's just the square root.

Variance is more useful when:

• The downstream calculation is itself squared (portfolio variance, covariance matrices).
• You're working with a sum of variances (which only makes sense in squared units).

Common pitfalls

• Population vs sample variance. Wickra emits population (/n); some libraries emit sample (/(n-1)). Multiply by n / (n-1) to convert.
• Squared units. Variance is in price-squared units; not directly comparable to price. Use StdDev for price-comparable volatility.

References

• Standard statistics text definition.

See also

• StdDev — square-root sibling.
• CoefficientOfVariation — variance-normalised-by-mean.
• MedianAbsoluteDeviation — robust alternative.
• Indicators-Overview — full taxonomy.