Fisher Transform: making turning points sharp

What it measures

The Fisher Transform normalises price into a band and then applies a mathematical transform that stretches the extremes, converting a distribution with fat tails into something closer to a bell curve.

The practical effect is that turning points, which are gradual in price, become sharp spikes in the indicator.

The reasoning behind it is that price distributions have far fatter tails than a bell curve, so extreme moves are much more common than a normal model expects. The transform stretches the middle and compresses nothing, which turns a gentle roll at the edge of a range into an abrupt reversal in the output.

How it is calculated

These are the steps Basis performs, verified against the published definition.

1. 1

   Normalise the median price to a −1 to +1 range against its highest and lowest values over the lookback.

2. 2

   Smooth that normalised value, then clamp it just inside ±1 — the transform diverges at exactly ±1.

3. 3

   Apply the transform: half the natural logarithm of (1 + value) divided by (1 − value).

4. 4

   Add half the previous transformed value, which smooths the output. The trigger line is the previous bar’s value.

Settings

Nine periods is the original. Longer windows make new extremes rarer, which reduces clamping and produces a calmer series with fewer spikes — but also removes most of the sharpness that is the reason to run this rather than a stochastic. There is little point lengthening it past the point where the transform stops doing anything visible.

How to read it

• Crossings of the trigger line are the signal, and they are unusually crisp compared with other oscillators.
• Extreme spikes mark points where price reached the edge of its recent range, which the transform then exaggerates.
• The indicator is unbounded in principle but practically clamped, so extremes are more common than a Gaussian would suggest.
• It is a range-position measure underneath the transform, which means it saturates in a trend exactly as the stochastic does — sharp turns in a market making continuous new highs are usually the indicator, not the market.

Where it misleads

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