zeonta.fisher_transform() — Ehlers’ Fisher Transform: normalized price reshaped to sharpen its turning points.
What it measures
Ordinary price data has a roughly uniform-to-bimodal distribution, not the Gaussian (bell-curve) one most statistical tools quietly assume. Ehlers’ insight was to reshape a normalised price into something close to Gaussian — under that reshaping, large deviations become genuinely rare events instead of routine noise, which is exactly what makes the transform’s turning points sharper and more decisive than an oscillator built directly from price.
Formula
Position = (Price - LowestPrice(n)) / (HighestPrice(n) - LowestPrice(n)) - 0.5; Value1 = 0.33 x 2 x Position + 0.67 x Value1[t-1], clamped to +/-0.999; Fish = 0.5 x ln((1 + Value1) / (1 - Value1)) + 0.5 x Fish[t-1]
Parameters
Required inputs: high, low
| Parameter | Default |
|---|---|
length |
10 |
Returns
| Column |
|---|
FISHERT_10 |
FISHERTs_10 |
Usage
Examples run against the 300-bar OHLCV fixture in tests/data/ohlcv.csv, loaded as df. The output shown is the real output.
import pandas as pd
import zeonta
df = pd.read_csv('tests/data/ohlcv.csv', parse_dates=['date']).set_index('date')
zeonta.fisher_transform(df['high'], df['low']).tail(3)
FISHERT_10 FISHERTs_10
date
2024-10-25 -0.813408 -0.884008
2024-10-26 -0.951520 -0.813408
2024-10-27 -1.273442 -0.951520
Accessor form: df.zta.fisher_transform(...)
How to read it
Read FISHERT/FISHERTs as a crossover pair the same way macd’s line and signal are read: the sharpness Ehlers built into this transform means the crossovers tend to occur right at genuine turning points rather than lagging behind them the way a rounded indicator like macd does.
Pitfalls
The sharp, decisive turns are a direct consequence of amplifying values near the edge of the recent range — on a genuinely choppy, range-bound market this can mean more frequent, less meaningful crossovers rather than fewer, cleaner ones.
Reference
Formula source: https://www.mesasoftware.com/papers/UsingTheFisherTransform.pdf