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

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. |
Related Indicators & See Also
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.