Center of Gravity (CG) Oscillator

John Ehlers' Center of Gravity oscillator. Treats the most recent period prices as masses and reports the weighted "center" of that mass distribution, negated and offset so positive readings correspond to recent strength. Has zero lag at the cycle the period is tuned to — one of Ehlers' near-zero-lag oscillators.

Quick reference

Item	Value
Family	Ehlers / Cycle (DSP)
Input type	f64
Output type	f64
Output range	unbounded; centred near zero by construction
Default parameters	period is required (typical 10)
Warmup period	period
Interpretation	> 0 recent strength; < 0 recent weakness; near-zero-lag at period

Formula

num_t = Σ_{k=0..period-1} (1 + k) · price_{t-k}
den_t = Σ_{k=0..period-1} price_{t-k}

CG_t  = - num_t / den_t + (period + 1) / 2

The constant offset (period + 1) / 2 centres the oscillator around zero for a constant input. See crates/wickra-core/src/indicators/center_of_gravity.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 0	Rolling window length.

CenterOfGravity::new returns Error::PeriodZero for period == 0.

Inputs / Outputs

Indicator<Input = f64, Output = f64>. Python: CenterOfGravity(period).batch(prices) returns a 1-D np.ndarray with NaN in the warmup prefix. Node: same shape; update(value) returns number | null.

Warmup

warmup_period() == period. The window fills exactly at input period; first emission lands there.

Edge cases

• Constant input. num and den both proportional to the constant; num/den == (period+1)/2, so CG outputs 0.
• All-zero window. den == 0 would cause division by zero; the indicator returns None for that bar.
• Pure trend. CG drifts steadily away from zero — the oscillator's centring assumption is broken by long trends.
• Reset. reset() clears the rolling window and the last value.

Examples

Rust

use wickra::{BatchExt, CenterOfGravity, Indicator};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let prices: Vec<f64> = (0..50)
        .map(|i| 100.0 + (f64::from(i) * 0.3).sin() * 5.0)
        .collect();
    let mut cg = CenterOfGravity::new(10)?;
    println!("row 20 = {:?}", cg.batch(&prices)[20]);
    Ok(())
}

Python

import numpy as np
import wickra as ta

prices = 100 + np.sin(np.linspace(0, 15, 50)) * 5
cg = ta.CenterOfGravity(10)
print('warmup:', cg.warmup_period())  # 10
print('row 20:', cg.batch(prices)[20])

Node

const wickra = require('wickra');
const cg = new wickra.CenterOfGravity(10);
const prices = Array.from({ length: 50 },
  (_, i) => 100 + Math.sin(i * 0.3) * 5);
console.log('row 20:', cg.batch(prices)[20]);

Streaming

use wickra::{CenterOfGravity, Indicator};

let mut cg = CenterOfGravity::new(10).unwrap();
let mut prev: Option<f64> = None;
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(v) = cg.update(px) {
        if let Some(p) = prev {
            if p < 0.0 && v > 0.0 { /* CG crossed up — bullish */ }
        }
        prev = Some(v);
    }
}

Interpretation

• Near-zero-lag oscillator. When period matches the dominant cycle, CG has very little lag — its peaks and troughs align with the price cycle's peaks and troughs, unlike RSI / Stochastic which lag by a quarter cycle.
• Zero-line crossings. Use as a fast cycle-momentum signal. Often paired with a slow trend filter (longer-period SMA, or Decycler) to gate the direction.
• Trend bias. In strong trends CG drifts away from zero; the oscillator centring breaks. Pair with a trend detector to mute signals during trends.

Common pitfalls

• Treating it as bounded. Output is unbounded; threshold-based systems need per-instrument calibration.
• Period mismatch with dominant cycle. CG's zero-lag property only holds at the cycle the period is tuned to. Combine with HilbertDominantCycle to find the right period — or use a fixed 10 and accept some lag outside that cycle band.
• Long warmup interpretation. During warmup (< period bars) no value is emitted; many Ehlers implementations show arbitrary fill values, which can be confused with real signal.

References

• John F. Ehlers, Cybernetic Analysis for Stocks and Futures (2004), ch. 7 — original Center of Gravity oscillator.

See also

• CyberneticCycle — sibling near-zero-lag cycle component.
• FisherTransform — paired with CG in many Ehlers charts.
• HilbertDominantCycle — for adaptive period selection.
• Indicators-Overview — full taxonomy.