Correlation Trend Indicator (CTI)

Summary

John F. Ehlers' Correlation Trend Indicator: the Pearson correlation of the last optInTimePeriod closes against a straight line of positive slope. Bounded in -1..+1 by construction — +1 is a perfectly linear uptrend, -1 a perfectly linear downtrend, 0 no linear trend. Trend strength and direction in one bounded number, with no smoothing, no recursion and no filter coefficients.

Arithmetically it is CORREL of the series against a ramp, with the ramp side collapsed to closed-form constants.

Chart

Reference data (CSV) · Chart (SVG)

Chart metadata i

Outputs

• outReal: line · zero · positive · negative

Formula

With n = optInTimePeriod, x the window's closes and y a straight line rising with time:

CTI = ( n·Σxy − Σx·Σy ) / sqrt( ( n·Σx² − (Σx)² ) · ( n·Σy² − (Σy)² ) ), or 0 when the window is flat

A rising series therefore reads positive. The y side is data-independent and collapses exactly: n·Σy² − (Σy)² = n²(n²−1)/12.

Notes

• A flat window returns exactly 0.0 rather than holding the previous value as the author's listing does; holding would make the function path-dependent.
• The result is clamped into -1..+1, as CORREL is: rounding in three sums can put a coefficient slightly outside its own range.
• optInTimePeriod starts at 2, not 1: at n = 1 the closed form n²(n²−1)/12 is identically zero and every window is degenerate.

Inputs

• inReal — The series to measure the trend of

Outputs

• outReal — Correlation against the ramp, in -1..+1

Parameters

Parameter	Type	Default	Accepted values	Description
optInTimePeriod	integer	20	2–100000	Number of trailing values correlated against the ramp

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

C

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

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

TA_Initialize();
TA_CTI( 0, n - 1, series, 20, &outBegIdx, &outNBElement, out );
printf( "%d values from bar %d; last out = %f\n", outNBElement, outBegIdx, out[outNBElement - 1] );

Rust

use ta_lib::Core;

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

let core = Core::new();
let range = core.cti(0, series.len() - 1, &series, 20, &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[] series = new double[252]; // your data, oldest first
double[] out = new double[252];

Core core = Core.DEFAULT;
OutRange r = core.cti(0, series.length - 1, series, 20, out);
System.out.println(r.count() + " values from bar " + r.begIdx() + "; last out = " + out[r.count() - 1]);

C#

using System;
using TALib;

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

var core = Core.Default;
OutRange r = core.Cti(0, series.Length - 1, series, 20, outReal);
Console.WriteLine($"{r.Count} values from bar {r.BegIdx}; last outReal = {outReal[r.Count - 1]}");

TypeScript

import { cti } from 'ta-lib';

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

const { begIdx, values } = cti(series, { timePeriod: 20 });
console.log(values.length + ' values from bar ' + begIdx + '; last values = ' + values[values.length - 1]);

Implementation

Added in 0.8.3 (ta-lib-python 0.8.3).

TA-Lib Definition: cti.c · cti.yaml

Native	File
C	ta_CTI.c
Rust	cti.rs
Java	Core_CTI.java
C#	Core_CTI.cs
TypeScript	cti.ts

Python: talib.CTI (ta-lib-python 0.8.3 or later), see ta-lib-python.

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

Aliases

Correlation Trend Indicator, Ehlers Correlation Trend Indicator, Correlation Trend

See Also

CORREL · LINEARREG_SLOPE · VHF

References

• John F. Ehlers, "Correlation As A Trend Indicator", Technical Analysis of Stocks & Commodities, V.38:5 (May 2020), Code Listing 1, author's PDF