QuanTAlib/lib/cycles/cg/cg.md

CG: Center of Gravity

"The market's center of mass reveals where momentum shifts before price does."

The Center of Gravity (CG) oscillator identifies potential turning points in price action using the physics concept of weighted center of mass. Developed by John Ehlers, it measures where the "weight" of prices is concentrated within a lookback window, providing leading signals for trend reversals with minimal lag.

Historical Context

John Ehlers introduced the Center of Gravity oscillator in his 2002 book Cybernetic Analysis for Stocks and Futures. Ehlers, an electrical engineer turned trader, applied signal processing concepts to financial markets, focusing on creating indicators with minimal lag.

The CG oscillator draws directly from physics: just as the center of gravity of an object determines its balance point, the CG of price determines where momentum is balanced within a window. Ehlers designed it to be a leading indicator, contrasting it with the inherent lag of traditional moving averages.

Architecture & Physics

The indicator calculates a weighted center of mass that oscillates around zero using a sliding window.

1. Weighted Sum (Numerator)

Num = \sum_{i=1}^{n} i \cdot P_{t-n+i}

where i ranges from 1 (oldest) to n (newest), giving more weight to recent data.

2. Simple Sum (Denominator)

Den = \sum_{i=1}^{n} P_{t-n+i}

3. Center of Gravity

CG_t = \frac{Num}{Den} - \frac{n + 1}{2}

The term \frac{n + 1}{2} represents the geometric center of the window, centering the indicator around zero.

Performance Profile

Operation Count (Streaming Mode, per Bar)

Operation	Count	Cost (cycles)	Subtotal
ADD (running sum update)	2	1	2
SUB (oldest value removal)	2	1	2
MUL (weight × price)	1	3	3
DIV (Num / Den)	1	15	15
Total	6	—	~22 cycles

Complexity Analysis

• Streaming: O(1) per bar using running sums
• Memory: O(n) for RingBuffer storage
• Warmup: n bars required

Validation

Library	Status	Notes
TA-Lib	N/A	Not standard in TA-Lib
Skender	N/A	Not standard in Skender.Stock.Indicators
PineScript	✅	Validated against ta.cg()

Usage & Pitfalls

• Zero crossing signals shift in momentum balance—bullish when crossing up, bearish when crossing down
• Positive values indicate weight concentrated in recent prices (uptrend)
• Negative values indicate weight concentrated in older prices (downtrend)
• Period of 10 is standard—smaller periods increase noise, larger periods add lag
• Strong trends cause CG to hang at extremes; wait for zero crossing for reversal confirmation
• Pair with trigger line (1-bar delay or small SMA) to reduce whipsaws

API

classDiagram
    class Cg {
        +int Period
        +double Value
        +bool IsHot
        +Cg(int period)
        +Cg(ITValuePublisher source, int period)
        +TValue Update(TValue input, bool isNew)
        +void Reset()
    }

Class: Cg

Parameter	Type	Default	Range	Description
period	int	10	>0	Lookback window for CG calculation

Properties

• Value (double): The current CG value (oscillates around 0)
• IsHot (bool): Returns true when warmup period is complete

Methods

• Update(TValue input, bool isNew): Updates the indicator with a new data point

C# Example

using QuanTAlib;

// Create a 10-period CG indicator
var cg = new Cg(period: 10);

// Update with streaming data
foreach (var bar in quotes)
{
    var result = cg.Update(new TValue(bar.Date, bar.Close));
    
    if (cg.IsHot)
    {
        Console.WriteLine($"{bar.Date}: CG = {result.Value:F4}");
        
        // Signal detection
        if (result.Value > 0 && cg.Previous.Value <= 0)
            Console.WriteLine("  → Bullish crossover");
    }
}

// Batch calculation
var output = Cg.Calculate(sourceSeries, period: 10);