Decycler Oscillator

Difference between a fast and a slow Decycler. Removes the trend component that both decyclers share, leaving the medium-frequency cycle band — analogous in spirit to MACD but with Ehlers' zero-lag high-pass filters instead of EMAs. Crosses zero at trend changes.

Quick reference

Item	Value
Family	Ehlers / Cycle (DSP)
Input type	f64
Output type	f64
Output range	unbounded; centred near zero
Default parameters	fast, slow both required (typical (10, 30))
Warmup period	2 (uses input directly until both decyclers fill)
Interpretation	> 0 cycle-band above trend; < 0 below; zero-cross signals shift

Formula

fast_dc_t = Decycler(fast).update(x_t)
slow_dc_t = Decycler(slow).update(x_t)

DecyclerOsc_t = fast_dc_t - slow_dc_t

fast < slow is required. See crates/wickra-core/src/indicators/decycler_oscillator.rs.

Parameters

Name	Type	Default	Constraint	Description
fast	usize	none	> 1, < slow	Fast Decycler critical period.
slow	usize	none	> 1, > fast	Slow Decycler critical period.

DecyclerOscillator::new returns Error::PeriodZero if either period is zero, and Error::InvalidPeriod { message: "fast period must be strictly less than slow period" } if fast >= slow.

Inputs / Outputs

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

Warmup

warmup_period() == 2. Both inner Decyclers use the pass-through- input initial condition for the first 2 bars; from bar 3 the recursions run.

Edge cases

• Constant input. Both Decyclers converge to the constant; difference converges to zero.
• Zero crossings. Treat as cycle-momentum direction changes, not as buy/sell signals on their own.
• Reset. reset() clears both inner decyclers.

Examples

Rust

use wickra::{BatchExt, DecyclerOscillator, 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 dco = DecyclerOscillator::new(10, 30)?;
    println!("row 50 = {:?}", dco.batch(&prices)[50]);
    Ok(())
}

Python

import numpy as np
import wickra as ta

prices = 100 + np.sin(np.linspace(0, 36, 120)) * 5
dco = ta.DecyclerOscillator(10, 30)
print('row 50:', dco.batch(prices)[50])

Node

const wickra = require('wickra');
const dco = new wickra.DecyclerOscillator(10, 30);
const prices = Array.from({ length: 120 },
  (_, i) => 100 + Math.sin(i * 0.3) * 5);
console.log('row 50:', dco.batch(prices)[50]);

Streaming

use wickra::{DecyclerOscillator, Indicator};

let mut dco = DecyclerOscillator::new(10, 30).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) = dco.update(px) {
        if let Some(p) = prev {
            if p < 0.0 && v > 0.0 { /* bullish zero cross */ }
            if p > 0.0 && v < 0.0 { /* bearish zero cross */ }
        }
        prev = Some(v);
    }
}

Interpretation

• Cycle-band oscillator. Captures the price action between the fast and slow cycle cutoffs. Default (10, 30) covers the 10-30 bar cycle band — Ehlers' typical "tradable cycle" range.
• Zero-cross signals. Use as a momentum-shift trigger similar to MACD's signal-line crossings, with the benefit of zero phase lag at trend frequencies.
• Vs MACD. Decycler oscillator has flatter response in the trend regime (because the trend cancels out) and sharper detection of mid-frequency cycle changes. MACD-style EMAs lag the trend; Ehlers' high-passes don't.

Common pitfalls

• Swapped periods. fast >= slow is rejected. The constructor errors clearly, but it's a common bug when reading parameters from config files.
• Treating it as bounded. Output is unbounded; thresholds (±0.5, ±1.0) are arbitrary and instrument-dependent.
• Mismatched fast/slow spacing. (10, 12) gives a very narrow band — output is mostly noise. Use at least a 2:1 ratio ((10, 20) or (10, 30)).

References

• John F. Ehlers, Cycle Analytics for Traders, Wiley (2013), ch. 4 — Decycler difference construction.

See also

• Decycler — the building block.
• RoofingFilter — alternative cycle-band extractor.
• MacdIndicator — EMA-based cousin.
• Indicators-Overview — full taxonomy.