RollingCovariance

Rolling covariance of the period-over-period returns of two series — the raw building block behind correlation, beta and portfolio variance.

Quick reference

Field	Value
Family	Price Statistics
Input type	(f64, f64) (a pair of levels x, y)
Output type	f64
Output range	unbounded; carries the product of the two return units
Default parameters	period is required (>= 2)
Warmup period	period + 1
Interpretation	Positive → returns move together; negative → they offset; magnitude scales with volatility.

Formula

Each update takes one (x, y) level pair, differences each channel into a one-step return, and reports the population covariance of those returns over the trailing window of period return pairs:

rxₜ = xₜ − xₜ₋₁          ryₜ = yₜ − yₜ₋₁
cov = (1/n) · Σ rx·ry − r̄x · r̄y

Unlike RollingCorrelation the result is not normalised to [−1, 1]: it carries the units of the two return streams multiplied together, so it scales with volatility. It is the raw building block behind correlation, beta and portfolio variance — positive when the two return streams tend to move the same way, negative when they offset.

Source: crates/wickra-core/src/indicators/rolling_covariance.rs.

Parameters

Name	Type	Default	Valid range	Source	Description
period	usize	none	>= 2	rolling_covariance.rs:61	Look-back window of return pairs. < 2 errors with Error::InvalidPeriod.

Inputs / Outputs

From crates/wickra-core/src/indicators/rolling_covariance.rs:

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

Python streams as update(x, y) -> float | None and batches over two equal-length arrays. Node streams as update(x, y) and batches over x[], y[].

Warmup

warmup_period() == period + 1. The first level in each channel produces no return, so a period-pair covariance needs one extra observation. The unit test accessors_and_metadata pins warmup_period() == 15 for period = 14; warmup_needs_period_plus_one pins the first Some at the period + 1-th pair.

Edge cases

• Co-moving returns. Two return streams that rise and fall together produce a positive covariance; offsetting streams a negative one.
• Independent / flat returns. When one channel has constant returns the covariance is 0; pinned by the module's zero-covariance test.
• Magnitude scales with volatility. Doubling one channel's returns doubles the covariance — it is unnormalised by design.
• Reset. reset() clears the return window and the previous levels.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut rc = RollingCovariance::new(14)?;
    // y = 3*x with varying x -> positive return covariance.
    let pairs: Vec<(f64, f64)> = (0..40)
        .map(|t| {
            let x = 100.0 + (f64::from(t) * 0.7).sin();
            (x, 3.0 * x)
        })
        .collect();
    let last = rc.batch(&pairs).into_iter().flatten().last().unwrap();
    println!("{last:.6}");
    Ok(())
}

Output:

0.636114

Python

import numpy as np
import wickra as ta

t = np.arange(40)
x = 100.0 + np.sin(t * 0.7)
y = 3.0 * x
print(round(ta.RollingCovariance(14).batch(x, y)[-1], 6))

Output:

0.636114

Node

const ta = require('wickra');
const x = Array.from({ length: 40 }, (_, t) => 100 + Math.sin(t * 0.7));
const y = x.map((v) => 3 * v);
console.log(new ta.RollingCovariance(14).batch(x, y).at(-1).toFixed(6));

Output:

0.636114

Interpretation

RollingCovariance is the term that sits inside almost every two-asset risk calculation: portfolio variance w₁²σ₁² + w₂²σ₂² + 2w₁w₂·cov, the CAPM beta cov(a, m) / var(m), and the numerator of correlation. Track it directly when you need the magnitude of co-movement, not just its sign — a covariance that grows even as correlation stays flat means both legs got more volatile together. When you want a scale-free number in [−1, 1], normalise via RollingCorrelation.

Common pitfalls

• Not comparable across pairs. Because covariance carries units, its raw magnitude cannot be compared between pairs with different volatilities — use correlation for that.
• Population, not sample. The estimator divides by n, not n − 1; for small windows the two conventions differ noticeably.

References

The covariance is the second mixed central moment; see any statistics text, e.g. Casella & Berger, Statistical Inference.

See also

• Indicator-RollingCorrelation — the normalised version in [−1, 1].
• Indicator-Beta — cov(a, b) / var(b) on returns.
• Indicators-Overview — the full taxonomy.