Pearson's Correlation Coefficient (r) (CORREL)

Summary

Pearson's correlation coefficient (r) between two input series over a rolling window of optInTimePeriod bars. Measures how linearly the two series move together. r near +1: strong positive co-movement; near -1: strong inverse; near 0: no linear relationship.

Chart

Reference data (CSV) · Chart (SVG)

Chart metadata i

Outputs

outReal: line · zero · positive · negative

Formula

r = (sumXY - sumX*sumY/n) / sqrt((sumX2 - sumX^2/n) * (sumY2 - sumY^2/n)), n = optInTimePeriod, sums over the window

Notes

When the correlation is undefined for a window (for example a constant series), the output is 0 rather than an error or NaN.

Inputs

inReal0 — First data series (X)
inReal1 — Second data series (Y)

Outputs

outReal — Correlation coefficient r in [-1, 1]

Parameters

Parameter	Type	Default	Accepted values	Description
`optInTimePeriod`	integer	30	1–100000	Rolling window length

Properties

Numerical Stability: Start-Independent


☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Display Shift


☐ Can Output NaN or ±Inf
☐ Identity at Period 1
☐ Uses Transcendental
☐ Input Must Be Positive

Example

#include <stdio.h>
#include <ta_libc.h>

int n = 252;
double series0[252]; /* your data, oldest first */
double series1[252]; /* your data, oldest first */
double out[252];
int outBegIdx, outNBElement;

TA_Initialize();
TA_CORREL( 0, n - 1, series0, series1, 30, &outBegIdx, &outNBElement, out );
printf( "%d values from bar %d; last out = %f\n", outNBElement, outBegIdx, out[outNBElement - 1] );

Rust

use ta_lib::Core;

let series0 = vec![0.0; 252]; // your data, oldest first
let series1 = vec![0.0; 252]; // your data, oldest first
let mut out = vec![0.0; 252];

let core = Core::new();
let range = core.correl(0, series0.len() - 1, &series0, &series1, 30, &mut out)?;
println!("{} values from bar {}; last out = {}", range.count, range.beg_idx, out[range.count - 1]);

Java

import io.github.talib.Core;
import io.github.talib.OutRange;

double[] series0 = new double[252]; // your data, oldest first
double[] series1 = new double[252]; // your data, oldest first
double[] out = new double[252];

Core core = Core.DEFAULT;
OutRange r = core.correl(0, series0.length - 1, series0, series1, 30, out);
System.out.println(r.count() + " values from bar " + r.begIdx() + "; last out = " + out[r.count() - 1]);

using System;
using TALib;

var series0 = new double[252]; // your data, oldest first
var series1 = new double[252]; // your data, oldest first
var outReal = new double[252];

var core = Core.Default;
OutRange r = core.Correl(0, series0.Length - 1, series0, series1, 30, outReal);
Console.WriteLine($"{r.Count} values from bar {r.BegIdx}; last outReal = {outReal[r.Count - 1]}");

TypeScript

import { correl } from 'ta-lib';

const series0 = new Float64Array(252); // your data, oldest first
const series1 = new Float64Array(252); // your data, oldest first

const { begIdx, values } = correl(series0, series1, { timePeriod: 30 });
console.log(values.length + ' values from bar ' + begIdx + '; last values = ' + values[values.length - 1]);

Implementation

Added in 0.4.0.

TA-Lib Definition: correl.c · correl.yaml

Native	File
C	`ta_CORREL.c`
Rust	`correl.rs`
Java	`Core_CORREL.java`
C#	`Core_CORREL.cs`
TypeScript	`correl.ts`

Python: talib.CORREL, see ta-lib-python.

TA-Lib is also available for R and more using a wrapper.

Aliases

Pearson Correlation, Correlation Coefficient, r

References

Karl Pearson