Fisher Transform

What is the Fisher Transform?

The Fisher Transform is John Ehlers' technique for reshaping price data into an approximately Gaussian (normal) distribution. It first rescales price, typically the bar midpoint, into a -1 to +1 range over a short lookback window (10 bars in Ehlers' original article), a smoothed form of min-max scaling, then applies the transform: half the natural logarithm of the ratio (1 + x) / (1 - x), with the input capped just inside ±1 so the logarithm stays finite. The effect is to stretch the tails: mid-range readings stay small, while readings near the extremes expand into sharp, isolated peaks.

Ehlers' argument was that price is not normally distributed, so turning points in ordinary oscillators come out rounded and mushy. After the transform, extreme values are rare and reversals show up as sharp slope changes. The standard signal set reflects that: the Fisher line crossing its own one-bar-delayed copy, plus extreme absolute readings marking stretched conditions, rather than fixed overbought/oversold lines.

How traders use it

• As a turn timer: the classic trigger is the Fisher line crossing its one-bar-delayed signal line after an extreme reading, which tends to print earlier (and more often) than signals from heavily smoothed oscillators.
• As a stretch detector: because the transformed values are approximately Gaussian, large absolute readings are statistically unusual, so traders treat them as zones to tighten stops, take profits, or watch for reversal, not as automatic fades.
• As a preprocessing step: the same transform is applied to other oscillators to sharpen their turns, while its counterpart, the Inverse Fisher Transform, does the opposite job and compresses an oscillator toward binary extremes.