Pearson Correlation

Rolling Pearson correlation between two synchronised series. Measures linear association on a [-1, +1] scale. +1 = perfect positive linear relationship; -1 = perfect negative; 0 = no linear relationship.

Quick reference

Item	Value
Family	Price Statistics
Input type	(f64, f64) — (x, y) pair per update
Output type	f64
Output range	[-1, +1]
Default parameters	period required
Warmup period	period
Interpretation	Linear association strength

Formula

cov_xy  = (1/n) · Σ x·y - x̄·ȳ
var_x   = (1/n) · Σ x² - x̄²
var_y   = (1/n) · Σ y² - ȳ²
Pearson = cov_xy / √(var_x · var_y)

Each update is O(1) via running sums. See crates/wickra-core/src/indicators/pearson_correlation.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 1	Rolling window.

Inputs / Outputs

Indicator<Input = (f64, f64), Output = f64>. Python: PearsonCorrelation(period).batch(x, y) returns 1-D np.ndarray.

Warmup

warmup_period() == period.

Edge cases

• Zero variance. Either input flat → denominator zero → output 0.0 (rather than NaN).
• Pearson on monotone series. Returns can be near ±1 even if the relationship is nonlinear, as long as ranks are monotone — for nonlinear relationships use SpearmanCorrelation.
• Reset. Clears running sums.

Examples

Rust

use wickra::{Indicator, PearsonCorrelation};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut p = PearsonCorrelation::new(50)?;
    for i in 0..100 {
        let x = f64::from(i);
        let y = x * 2.0 + (f64::from(i) * 0.5).sin();
        let _ = p.update((x, y));
    }
    Ok(())
}

Python

import numpy as np
import wickra as ta

x = np.arange(100, dtype=float)
y = x * 2 + np.sin(np.linspace(0, 50, 100))
p = ta.PearsonCorrelation(50)
print(p.batch(x, y)[-1])

Node

const wickra = require('wickra');
const p = new wickra.PearsonCorrelation(50);
// feed x, y

Streaming

use wickra::{Indicator, PearsonCorrelation};

let mut p = PearsonCorrelation::new(252).unwrap();
let price_stream: Vec<(f64, f64)> = Vec::new(); // your paired (a, b) feed
for (asset_a, asset_b) in price_stream {
    if let Some(v) = p.update((asset_a, asset_b)) {
        // v = rolling correlation
    }
}

Interpretation

• Pearson > 0.7. Strong positive linear relationship.
• Pearson 0.3 - 0.7. Moderate.
• Pearson < 0.3. Weak or absent.
• Diversification. Negative correlation between asset pairs is the basis of portfolio diversification — a -0.5 correlation pair smooths the joint equity curve significantly.

Common pitfalls

• Linear only. Detects linear association. Two series with perfect nonlinear relationship (e.g. y = x²) can have Pearson ≈ 0. Use Spearman for nonlinear.
• Period choice. Short windows produce noisy correlation estimates. ≥ 50 bars recommended.
• Pairs of returns vs prices. Correlation of returns is the finance-meaningful measure; correlation of raw prices is dominated by joint trends and overstates dependence.

References

• Karl Pearson, Notes on Regression and Inheritance in the Case of Two Parents, Proceedings of the Royal Society of London, 1895.

See also

• SpearmanCorrelation — rank- based cousin (handles monotone nonlinearities).
• Beta — slope rather than correlation.
• Autocorrelation — single-series cousin.
• Indicators-Overview — full taxonomy.