Hilbert Dominant Cycle

John Ehlers' Hilbert Transform–based Dominant Cycle period estimator. Decomposes price into in-phase and quadrature components via a truncated Hilbert transform, derives the instantaneous phase, and recovers the dominant cycle period from the phase rate of change. The result is clamped to the [6, 50] bar band Ehlers identifies as the meaningful tradable cycle range.

Quick reference

Item	Value
Family	Ehlers / Cycle (DSP)
Input type	f64
Output type	f64 — the estimated dominant cycle period in bars
Output range	[6, 50]
Default parameters	none — HilbertDominantCycle::new() takes no arguments
Warmup period	~50 bars (chain of smoothers must fill)
Interpretation	Adaptive period estimate for downstream cycle-aware oscillators

Formula

The truncated Hilbert transform pipeline (Ehlers' canonical form, matching TA-Lib's HT_DCPERIOD):

1. smooth   = WMA-4 of input
2. detrender = HT operator applied to smooth      (in-phase)
3. q1, i1   = HT-derived quadrature / in-phase
4. j_i, j_q = phase rotations
5. i2 = i1 - j_q;  q2 = q1 + j_i
6. re, im = smoothed in-phase/quadrature products
7. phase  = atan(im / re)
8. dp     = phase_{t-1} - phase_t   (clamped >= 1, <= 60)
9. period = median-smoothed dp
10. period = clamp(period, 6, 50)

The smoothers and detrenders need ~6 bars of history each, so the chain takes ~50 inputs to stabilise. See crates/wickra-core/src/indicators/hilbert_dominant_cycle.rs.

Parameters

No parameters. HilbertDominantCycle::new() returns a default- constructed estimator; Default is also implemented.

Inputs / Outputs

Indicator<Input = f64, Output = f64>. Python: HilbertDominantCycle().batch(prices) returns a 1-D np.ndarray with NaN in the long warmup prefix. Node: same shape; update returns number | null.

Warmup

Conservative warmup_period() ~50 bars. The first non-None emission typically lands earlier, but the early outputs are noisy until the median smoothing settles.

Edge cases

• Constant input. Phase is undefined; dp clamps to its lower bound and the period reads at the upper clamp (50).
• Pure sinusoid. The estimator locks to the sinusoid's period within ~2 cycles of warmup; on a 20-bar sinusoid the output hovers near 20.
• Trending input. Phase rotates slowly; period reads near the upper end of [6, 50].
• Output clamp. Values outside [6, 50] are clamped — Ehlers' rationale is that periods outside this band are not tradable cycles (too noisy below 6, indistinguishable from trend above 50).
• Reset. reset() clears all internal buffers and the last value.

Examples

Rust

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

fn main() {
    let prices: Vec<f64> = (0..300)
        .map(|i| 100.0 + (f64::from(i) * 2.0 * std::f64::consts::PI / 20.0).sin() * 5.0)
        .collect();
    let mut ht = HilbertDominantCycle::new();
    let out = ht.batch(&prices);
    println!("row 200 (expected ~20): {:?}", out[200]);
}

Python

import numpy as np
import wickra as ta

# 20-bar sinusoid
t = np.arange(300)
prices = 100 + np.sin(t * 2 * np.pi / 20) * 5
ht = ta.HilbertDominantCycle()
out = ht.batch(prices)
print('row 200 period estimate:', out[200])  # expected ~20

Node

const wickra = require('wickra');

const ht = new wickra.HilbertDominantCycle();
const prices = Array.from({ length: 300 },
  (_, i) => 100 + Math.sin(i * 2 * Math.PI / 20) * 5);
console.log('row 200:', ht.batch(prices)[200]);

Streaming

use wickra::{HilbertDominantCycle, Indicator, Rsi};

let mut ht = HilbertDominantCycle::new();
let mut period_history: Vec<f64> = Vec::new();
let price_stream: Vec<f64> = Vec::new(); // your live price feed
for px in price_stream {
    if let Some(p) = ht.update(px) {
        period_history.push(p);
        // Feed half-period into an adaptive oscillator
        let adapt = (p * 0.5).round() as usize;
        // ... e.g. recreate Rsi::new(adapt.max(3))
    }
}

Interpretation

• Adaptive period estimator. The standard use is to feed half the dominant period into a period-adaptive oscillator (RSI, Stoch, CCI). See AdaptiveCycle for a wrapper that does exactly this.
• Regime indicator. A period reading at the 50 clamp signals a trending or aperiodic market; a stable period in the 15-30 range indicates a cyclical regime where mean-reversion strategies work.
• Reference for backtesting. Pinning the period at, say, 20 in a backtest then comparing to the live HilbertDominantCycle reading shows whether the parameter was actually well-tuned for the market state.

Common pitfalls

• Treating it as a price indicator. The output is period, not price. Don't plot it on a price chart's main panel.
• Long warmup expectations. ~50 bars before usable, ~100 bars before stable. Backtests under 200 bars get only transient output.
• Clamp masking. Many cycle-detection failures end up at the 50 clamp. If your output is always 50, the price probably isn't periodic — don't read the clamp value as a meaningful cycle.

References

• John F. Ehlers, Rocket Science for Traders (2001), ch. 7 — the truncated Hilbert transform construction.
• John F. Ehlers, Cybernetic Analysis for Stocks and Futures (2004) — refined median-smoothing approach used here.

See also

• AdaptiveCycle — half-period wrapper for adaptive oscillators.
• Mama — uses the same phase machinery for adaptive smoothing.
• SineWave — sine + leadsine from the same phase estimate.
• Indicators-Overview — full taxonomy.