Center of Gravity Oscillator (CG)

Summary

John Ehlers' Center of Gravity oscillator: the balance point of the last optInTimePeriod values, each weighted by its value and placed at its position counting back from the current bar, which is position 1, negated so that it rises with price. It is smooth and has essentially no lag. Ehlers reads turning points from it and trades its crossings with a copy of itself delayed by one bar. For a positive series it stays between -optInTimePeriod and -1, and a flat window sits at the midpoint, -(optInTimePeriod+1)/2.

Formula

$$\mathrm{CG}_t = -\frac{\sum_{i=0}^{n-1} (i+1)\,X_{t-i}}{\sum_{i=0}^{n-1} X_{t-i}}, \text{ or } -\frac{n+1}{2} \text{ when } \sum_{i=0}^{n-1} X_{t-i} = 0$$

where $X$ is the input series, $n$ is optInTimePeriod and $i$ counts bars back from the current bar, which carries the smallest weight.

Notes

• Ehlers' default input is the median price (H+L)/2: pass the output of MEDPRICE to reproduce it.
• His 2004 book presents the same oscillator shifted up by (optInTimePeriod+1)/2, so that a flat window reads 0: add (optInTimePeriod+1)/2 to the output to obtain that form.
• Where the window sums to exactly zero the author's listing keeps its previous value; TA-Lib returns -(optInTimePeriod+1)/2, so every value depends on its own window alone.
• Both sums are exact before the divide, so a window summing to exactly zero is always recognised and the value does not depend on where the call started. The exception is a window holding a non-finite value, a value with bits below 2^-1022 (every subnormal, and only values under about 2e-292), or values that together span more binary digits than the sums can hold exactly (97 at the default period, 84 at 1000, 58 at 100000): it is summed in floating point, oldest value first.

Inputs

• inReal — The series to measure

Outputs

• outReal — Negated center of gravity of the window

Parameters

Parameter	Type	Default	Accepted values	Description
optInTimePeriod	integer	10	2–100000	Number of bars in the window

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: cg.c · cg.yaml

Native	File
C	ta_CG.c
Rust	cg.rs
Java	Core_CG.java
C#	Core_CG.cs

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

Aliases

Center of Gravity Oscillator, COG

See Also

WMA · MEDPRICE · CTI

References

• John F. Ehlers, "The CG Oscillator", MESA Software, author's PDF; published as "The Center Of Gravity Oscillator", Technical Analysis of Stocks & Commodities, May 2002
• John F. Ehlers, Cybernetic Analysis for Stocks and Futures, Wiley, 2004, chapter 5