What Is the Fisher Transform?
Fisher transform is an indicator that applies a mathematical transformation to normalised price, converting a distribution with fat tails into one closer to a bell curve. Extremes become visually sharper, but the transformation adds no information the underlying price did not already contain.
Covered on this page: TradingView.
The Fisher transform takes a price series that has been squeezed into a fixed range and reshapes its distribution. The result looks dramatically more decisive than the input, which is the whole appeal and also the whole problem.
How it works
First the price is normalised. The high and low of a lookback window define a range, and the current price is expressed as a position inside it, between minus one and plus one.
Then the transform is applied. The formula is half the natural logarithm of one plus the value divided by one minus the value, which is the inverse hyperbolic tangent.
That function is nearly flat in the middle and very steep at the edges. A normalised value moving from 0.90 to 0.95 produces a far larger change in output than one moving from 0.10 to 0.15.
What the reshaping does and does not do
The stated purpose is distributional. Price returns have fatter tails than a normal distribution, and the transform pushes the shape closer to a bell curve so that extreme readings are rarer and carry more weight.
That part is genuinely true of the output. What it does not do is make the input more informative - the transform is a monotonic function, so the order of the readings is exactly the order of the normalised values that produced them.
A monotonic function cannot reorder anything. If the raw reading was the highest of the last hundred bars, the transformed reading is also the highest - and any threshold crossing on one has a corresponding crossing on the other.
A worked example
Take a ten-bar lookback. Price closes at the top of its ten-bar range, so the normalised value is close to plus one.
The transform sends that near the vertical. As the normalised input approaches one, the output grows without bound, which is why implementations clamp the input just short of the limit.
The chart now shows a dramatic spike. The underlying fact is unchanged: price closed at the top of a ten-bar range, which happens regularly and on this site’s series is not a rare event at all.
So the spike measures the steepness of a logarithm, not the unusualness of the market. Both things are on the screen and only one of them is about price.
The original data
On this site’s shared series: median bar range 0.493, ninetieth percentile 1.101, largest bar 2.338. Direction runs average 2.01 bars with a longest of 11. A round trip costs 0.0098, about 2% of the median bar range.
Direction changing every two bars is what fills a short lookback with extremes. A ten-bar window is refreshed constantly, so closing at the top or bottom of it is ordinary rather than exceptional.
And the round trip is 2% of a typical bar. An indicator that produces visually emphatic signals in ordinary conditions is an indicator that invites paying that cost often, which is the practical risk the sharpened display creates.
Where it came from
The transform was introduced by John Ehlers, an engineer who spent his career in signal processing before applying the same methods to market data, and who wrote it up in his book on cybernetic analysis.
That origin explains the design. In signal processing, reshaping a distribution before feeding it into a filter is routine housekeeping - the filter behaves better when its input matches the assumptions it was built on.
The step was never meant to be the signal. It was preparation for one, and the indicator became popular as a standalone reading rather than as the preprocessing stage it was written to be.
Which is a common fate for borrowed engineering. The method is sound in the context it came from, and what travelled to charting platforms was the picture rather than the purpose.
Sharpness is a display property
Visual emphasis changes behaviour. A reading drawn as a violent spike is acted on more readily than the same reading drawn as a modest rise, even when the two describe identical price.
That is worth naming rather than assuming away. The transform’s benefit is described in statistical language, and its actual effect on most users is a change in how confident the chart looks.
The statistical argument has a real audience. Somebody building a system that assumes normally distributed inputs has a reason to reshape the distribution before feeding it in.
Somebody reading the chart by eye does not. For that user the transform trades a gentle curve for a steep one and supplies nothing else, and knowing which of those two people you are is the whole decision.
When it fails
The characteristic failure is mistaking steepness for significance. The output goes nearly vertical at the extremes, so an ordinary reading at the edge of a short lookback is drawn as a dramatic event.
The trader sees an unmistakable signal and acts on it. What actually happened was price closing near the top of a ten-bar range - something this site’s series does constantly. The drama came from the logarithm, and the logarithm knows nothing about the market.
A second failure is using too short a lookback, which puts the reading at an extreme almost every bar.
A third is treating it as leading. The normalisation window is built from past bars and the transform adds nothing forward-looking.
A fourth is trading the crossings of fixed levels, which are arbitrary once the scale is unbounded.
And a fifth is running it alongside a stochastic and calling it confirmation. They are the same measurement with different arithmetic applied afterwards, so agreement between them is arithmetic rather than evidence.
Related
Stochastic covers the normalised input this is usually built from. RSI covers the other bounded oscillator people compare it to. And moving average covers the smoothing most implementations apply to the output.
This is the clearest case I know of a tool that changes how something looks without changing what it is. The transform makes turns appear abrupt and obvious on screen. Run it and the untransformed version side by side and they turn on the same bars - one just looks more confident about it.
— Michael Whitman, from this video
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