Cybernetic Cycle Component

John Ehlers' Cybernetic Cycle Component (CCC). Detrends price via a 4-tap pre-smoother and an alpha-parameterised second-order high-pass recursion, leaving a near-zero-mean oscillator that tracks the dominant cycle component while filtering trend. Classic EasyLanguage construct from Cybernetic Analysis for Stocks and Futures (Ehlers 2004, ch. 4).

Quick reference

Item	Value
Family	Ehlers / Cycle (DSP)
Input type	f64
Output type	f64
Output range	unbounded; centred near zero
Default parameters	period is required (Ehlers' typical 10)
Warmup period	6
Interpretation	Cycle oscillator; zero crossings = cycle-momentum reversals

Formula

Pre-smoother + second-order recursion:

smooth_t = (x_t + 2·x_{t-1} + 2·x_{t-2} + x_{t-3}) / 6

alpha    = 2 / (period + 1)

cycle_t  = (1 - α/2)² · (smooth_t - 2·smooth_{t-1} + smooth_{t-2})
         + 2 · (1 - α) · cycle_{t-1}
         - (1 - α)² · cycle_{t-2}

The first six outputs follow Ehlers' "use the input directly" initial condition so downstream consumers stay reactive. See crates/wickra-core/src/indicators/cybernetic_cycle.rs.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 0	Dominant cycle period (α = 2 / (period + 1)).

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

Inputs / Outputs

Indicator<Input = f64, Output = f64>. Python: CyberneticCycle(period).batch(prices) returns a 1-D np.ndarray. Node: same shape; update(value) returns number.

Warmup

warmup_period() == 6. The first 6 outputs use the input directly; from bar 7 the recursion runs in earnest.

Edge cases

• Constant input. Smoother converges to the constant; cycle output decays to zero.
• Period vs alpha. Larger period → smaller alpha → slower cycle. period = 10 is Ehlers' typical EasyLanguage example.
• Pre-smoother coefficients. The 1, 2, 2, 1 4-tap filter is fixed (not configurable) — it's an Ehlers signature step.
• Reset. reset() clears all internal buffers and the bar counter.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let prices: Vec<f64> = (0..120)
        .map(|i| 100.0 + (f64::from(i) * 0.3).sin() * 5.0)
        .collect();
    let mut cc = CyberneticCycle::new(10)?;
    println!("row 30 = {:?}", cc.batch(&prices)[30]);
    Ok(())
}

Python

import numpy as np
import wickra as ta

prices = 100 + np.sin(np.linspace(0, 36, 120)) * 5
cc = ta.CyberneticCycle(10)
print('row 30:', cc.batch(prices)[30])

Node

const wickra = require('wickra');
const cc = new wickra.CyberneticCycle(10);
const prices = Array.from({ length: 120 },
  (_, i) => 100 + Math.sin(i * 0.3) * 5);
console.log('row 30:', cc.batch(prices)[30]);

Streaming

use wickra::{CyberneticCycle, Indicator};

let mut cc = CyberneticCycle::new(10).unwrap();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(v) = cc.update(px) {
        // Zero crossings = cycle-momentum reversals
    }
}

Interpretation

• Cycle-band oscillator. Captures the cycle component while filtering both trend (via the high-pass-like second-order difference) and noise (via the 4-tap pre-smoother).
• Zero crossings. Mark cycle-momentum reversals — bullish on cross up, bearish on cross down.
• Vs RoofingFilter / DecyclerOscillator. Cybernetic Cycle is more responsive (less lag) but slightly noisier. Roofing Filter has cleaner band-isolation; Decycler Oscillator has zero-phase-lag at trend frequencies.

Common pitfalls

• Treating output as bounded. Output amplitude scales with price-cycle amplitude; thresholds are instrument-dependent.
• Period mismatch with cycle. If the actual dominant cycle is far from period, the response is attenuated. Pair with HilbertDominantCycle to adapt the period dynamically (or use AdaptiveCycle).
• Warmup transients. The first 6 outputs aren't smoothed — consider them placeholder values, not signal.

References

• John F. Ehlers, Cybernetic Analysis for Stocks and Futures (2004), ch. 4 — Cybernetic Cycle definition.

See also

• CenterOfGravity — near-zero-lag sibling.
• DecyclerOscillator — zero-phase-lag alternative.
• RoofingFilter — band-isolation alternative.
• Indicators-Overview — full taxonomy.