Fisher Transform

John Ehlers' Fisher Transform of price. Normalises the most recent price to [-1, +1] via min/max over a period window, smooths the normalised value with a 0.33 / 0.67 IIR step, and applies the Fisher transform with Ehlers' own output smoothing, Fisher_t = 0.5 * ln((1+x)/(1-x)) + 0.5 * Fisher_{t-1}. The result has a near-Gaussian distribution, so extreme readings stand out cleanly — much more cleanly than the raw normalised price, whose distribution is heavy-tailed and hard to threshold consistently.

Quick reference

Item	Value
Family	Ehlers / Cycle (DSP)
Input type	f64
Output type	f64
Output range	±ln(1999) ≈ ±7.6 in the limit (clamp + feedback); typically within ±3
Default parameters	period is required (Ehlers' typical value 10)
Warmup period	period
Interpretation	Crossover with prior bar's value = signal; beyond ±2–3 is extreme

Formula

n_t  = 2 * (close_t - min(close, period)) / (max - min) - 1      (0 when max == min)
s_t  = clamp(0.33 * n_t + 0.67 * s_{t-1}, -0.999, +0.999)       (IIR smoothing)

Fisher_t = 0.5 * ln((1 + s_t) / (1 - s_t)) + 0.5 * Fisher_{t-1}

This is Ehlers' 2002 code: the 0.999 clamp avoids the singularity at ±1, and it is the clamped value that recurs as s_{t-1} (Ehlers overwrites Value1 after clamping). The 0.33 / 0.67 IIR is the classic Ehlers smoothing step, and the + 0.5 * Fisher_{t-1} term is Ehlers' half-weight carry of the previous output (seeded with 0 on the first emission). Because of that carry, a fully saturated input settles at ln((1 + 0.999) / (1 - 0.999)) = ln(1999) ≈ 7.6, double the single-step value. See crates/wickra-core/src/indicators/fisher_transform.rs.

A lagged "trigger" line — Fisher value one bar behind — is the canonical chart companion. Wickra exposes only the primary Fisher value; lag manually in user code if you need the trigger.

Parameters

Name	Type	Default	Constraint	Description
period	usize	none	> 0	Rolling min/max window length. Ehlers' typical: 10.

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

Inputs / Outputs

Indicator<Input = f64, Output = f64>. Python: FisherTransform(period).batch(prices) returns an array.array('d') with NaN for the warmup prefix. Node: same shape; update(close) returns number | null.

Warmup

warmup_period() == period. The rolling extrema window fills at exactly period inputs; the first emission lands on input period.

Edge cases

• Constant input. max == min → division by zero is avoided by treating the normalised value as 0. With a zero history the output is exactly 0 (no signal) — see constant_series_zero_range_yields_zero.
• Sudden gap. A single outlier dramatically widens the min/max range and pulls the normalised value toward ±1; the Fisher transform amplifies this near the saturation edges — useful for extreme-detection.
• Output rare-but-large excursions. The clamp plus the 0.5 * Fisher_{t-1} carry caps the output at ±ln(1999) ≈ ±7.6. On a random walk with period = 10, |Fisher| > 2 occurs about a quarter of the time and |Fisher| > 3 about 6% of the time; a reading beyond ±4 is unusual.
• Non-finite input. NaN / ±inf inputs return None and leave the state untouched (ignores_non_finite_input).
• Reset. reset() clears the rolling window, the smoothed accumulator, and the last value.

Examples

Rust

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

Python

import numpy as np
import wickra as ta

prices = 100 + np.sin(np.linspace(0, 36, 120)) * 5
ft = ta.FisherTransform(10)
out = ft.batch(prices)
print('warmup:', ft.warmup_period())  # 10
print('row 30:', out[30])

Node

const wickra = require('wickra');

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

Streaming

use wickra::{FisherTransform, Indicator};

let mut ft = FisherTransform::new(10).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) = ft.update(px) {
        if let Some(p) = prev {
            // Trigger-line crossover (Fisher cross of its 1-bar lag)
            if p < 0.0 && v > 0.0 { /* bullish cross */ }
            if p > 0.0 && v < 0.0 { /* bearish cross */ }
        }
        prev = Some(v);
    }
}

Interpretation

• Near-Gaussian distribution. Unlike raw RSI or stochastic, Fisher's output has fat-but-not-pathological tails. Because of Ehlers' 0.5 * Fisher_{t-1} carry the scale is roughly double the bare transform, so thresholds around ±2 / ±3 mark extremes.
• Trigger crossover. The classic two-line Fisher chart pairs the primary line against its 1-bar lag; a cross signals a momentum shift. Wickra omits the trigger line — bottle it yourself by caching the previous output.
• Trend-state vs cycle-state. In strong trends Fisher saturates at large readings and stays there for long stretches. In cycle regimes it oscillates rapidly with each bar — pair with a trend filter to pick the right interpretation.

Common pitfalls

• Too-short period. period = 3 makes Fisher track every wiggle — false signals dominate. Use 10 (Ehlers' default) or longer for daily bars.
• Treating the output like RSI. Fisher is unbounded and centred at zero, not 50. "Overbought above 70" makes no sense here.
• Trigger lag. A common bug is comparing the current Fisher value to itself ("Fisher > 0"). The classic signal is the crossover of the value and its 1-bar-lagged trigger.

References

• John F. Ehlers, Using the Fisher Transform, Technical Analysis of Stocks & Commodities, November 2002 — original.
• John F. Ehlers, Cybernetic Analysis for Stocks and Futures (2004) — extended treatment with parameter guidance.

See also

• InverseFisherTransform — algebraic inverse, applies the squashing wrapper instead.
• Rsi — the bounded oscillator Fisher is often layered onto.
• LaguerreRsi — alternative Ehlers momentum oscillator.
• Indicators-Overview — full taxonomy.