Center of Gravity Oscillator

Ehlers DSP oscillator momentum ehlers dsp zero-lag

The CG Oscillator identifies price turning points with essentially zero lag by calculating the balance point of prices.

Visual Example

Center of Gravity Oscillator — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-07-01 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

The CG Oscillator identifies price turning points with essentially zero lag by calculating the balance point of prices.

Use as a zero-lag momentum oscillator to detect cycle turning points. Crossovers of the trigger line provide high-accuracy entry and exit signals.

Part of QuantWave's Ehlers digital signal processing suite. Designed for low-lag cycle and trend work — pair with Roofing Filter or SuperSmoother on noisy inputs.

Ehlers introduces the Center of Gravity oscillator in Cybernetic Analysis (2004) as a near-zero-lag indicator. It computes the center of mass of a price series over a lookback window, producing an oscillator whose turning points lead price turns — a reversal of the usual indicator lag relationship.

Typical applications:

Use for cycle timing in mean-reverting regimes
Gate with Hurst exponent or ADX before taking cycle signals
Allow 10+ bars warm-up for filter state to stabilise
Chain with Roofing Filter when input is noisy

QuantWave implements this via the universal Next<T> trait — bit-identical across Rust streaming, Python streaming, and Polars .ta() batch plugins.

Formula / Specification

Implementation (quantwave-core/src/indicators/cg.rs):

\[ CG = -\frac{\sum_{i=0}^{N-1} (i+1) \times Price_i}{\sum_{i=0}^{N-1} Price_i} \]

Gold-standard parity vectors: quantwave-core/tests/gold_standard/cg.json.

Parameters

Parameter	Default	Description
`period`	10	Observation window length

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::CG;
use quantwave_core::traits::Next;

let mut ind = CG::new(10);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import CG

ind = CG(10)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_center_of_gravity_oscillator(series: pl.Series) -> pl.Series:
    ind = qw.CG(10)
    return pl.Series([ind.next(float(v)) for v in series.to_list()])

df = (
    pl.read_csv('ohlcv.csv')
    .lazy()
    .with_columns(
        pl.col("close").map_batches(apply_center_of_gravity_oscillator, return_dtype=pl.Float64).alias("center_of_gravity_oscillator")
    )
    .collect()
)

All surfaces are bit-identical via the single Next<T> implementation and proptests.

Edge Cases & Limitations

Recursive DSP filters require a warm-up period; first N bars may be unstable or raw-pass-through.
Designed for cyclic/mean-reverting regimes; trending markets can produce lag or drift.
Parameter period (or equivalent) controls cutoff — too small adds noise, too large adds lag.
Prefer chaining with other Ehlers tools (Roofing Filter, SuperSmoother) on noisy inputs.
Validated via proptests against gold-standard vectors where available.
No look-ahead bias; suitable for live streaming and batch feature pipelines.

Boundary Behavior

Condition	Behavior
Warm-up	Leading bars return NaN until warmup_bars is satisfied.
period > len	When period exceeds series length, output is all NaN.
NaN inputs	NaN in input propagates to output (NaN out).
Invalid params	Non-positive period or missing required params raise ValueError.
Empty data	Empty input returns an empty result series.

Sources & References

Primary Source: https://github.com/lavs9/quantwave/blob/main/references/Ehlers%20Papers/TheCGOscillator.pdf

Implementation: quantwave-core/src/indicators/cg.rs (CG / CG_METADATA). Parity: quantwave-core/tests/gold_standard/cg.json

Provenance: Standards bulk upgrade 2026-07-01 IST — see docs/DOCUMENTATION_STANDARDS.md.