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Cyber Cycle

Ehlers DSP cycle oscillator ehlers dsp

An oscillator introduced by John Ehlers that models the cyclical component of a time series using FIR smoothing.

Visual Example

Cyber Cycle — annotated preview mapping to core implementation

Synthetic ideal per library logic. Generated 2026-06-25 IST via docs/generate_all_previews.py (reproducible; maps to core Next<T> implementation).

Description

The Cyber Cycle indicator is a technical analysis tool that an oscillator introduced by john ehlers that models the cyclical component of a time series using fir smoothing.

This indicator is primarily used for identifying key market conditions. It provides a robust signal that can be easily integrated into both simple strategies and more complex machine learning feature pipelines. Compared to its alternatives, it offers a distinct balance of responsiveness and stability.

Traders often combine this with other metrics to confirm signals and avoid false positives during sideways market regimes. It remains a standard tool for systematic trading models.

Use as a high-resolution short-term cycle oscillator to time entries and exits around cycle turns. Pair with a trend classifier to suppress signals in trending conditions.

Ehlers introduces the Cyber Cycle in Cybernetic Analysis (2004) as a bandpass-like filter isolating the short-term cyclical component. The trigger line is the Cyber Cycle delayed by one bar, creating a clean crossover signal without derivative noise.

QuantWave implements this indicator via the universal Next<T> trait, guaranteeing bit-identical results between Rust streaming, Python streaming, and Polars batch (.ta() / map_batches) surfaces.

Formula / Specification

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

[ \alpha = \frac{2}{\text{Length} + 1} ] [ \text{Smooth} = \frac{X_t + 2X_{t-1} + 2X_{t-2} + X_{t-3}}{6} ] [ CC_t = \left(1 - \frac{\alpha}{2}\right)^2 (\text{Smooth}t - 2\text{Smooth}} + \text{Smooth{t-2}) + 2(1 - \alpha)CC ]} - (1 - \alpha)^2 CC_{t-2

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

Parameters

Parameter Default Description
length 14 Alpha smoothing length parameter

Usage Examples

Streaming (Rust)

use quantwave_core::indicators::CYBER_CYCLE;
use quantwave_core::traits::Next;

let mut ind = CYBER_CYCLE::new(14);
for price in &prices {
    let value = ind.next(price);
}

Streaming (Python)

from quantwave import CYBER_CYCLE

ind = CYBER_CYCLE(14)
for price in prices:
    value = ind.next(price)

Polars Batch (Python)

import polars as pl
import quantwave as qw

def apply_cyber_cycle(series: pl.Series) -> pl.Series:
    ind = qw.CYBER_CYCLE(14)
    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_cyber_cycle, return_dtype=pl.Float64).alias("cyber_cycle")
    )
    .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: Cybernetic Analysis for Stocks and Futures, John Ehlers, 2004, Chapter 4

Implementation: quantwave-core/src/indicators/cyber_cycle.rs (CYBER_CYCLE / CYBER_CYCLE_METADATA). Parity: quantwave-core/tests/gold_standard/cyber_cycle.json

Provenance: Standards bulk upgrade 2026-06-25 IST — see docs/DOCUMENTATION_STANDARDS.md.