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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.

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

ParameterTypeDefaultAccepted valuesDescription
optInTimePeriodinteger202–100000Number of trailing values correlated against the ramp

Properties

Numerical Stability: Start-Independent

☐ Overlap Input
✅ Independent Y-Axis i
☐ Candlestick
☐ Can Output NaN or ±Inf
☐ Identity at Period 1

Implementation

TA-Lib Definition: cti.c · cti.yaml

NativeFile
Cta_CTI.c
Rustcti.rs
JavaCore_CTI.java
C#Core_CTI.cs

TA-Lib is also available for Python, 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
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