# Gaussian Fisher Transform Price Reversals - FTR

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"This indicator shows you how to identify price reversals in a timely manner." John F. Ehlers

Introduction :

The Gaussian Fisher Transform Price Reversals indicator, dubbed FTR for short, is a stat based price reversal detection indicator inspired by and based on the work of the electrical engineer now private trader John F. Ehlers.

The Fisher Transform :

It is a common assumption that prices have a gaussian / normal probability density function(PDF), i.e. a sample of n close prices would be normally distributed if the probability of observing a price value say at any given standard deviation range is equal to that probability in the case of the normal distribution, e.g. 68% off all samples fell within one standard deviation around the mean, which is what we would expect if the data was normal.

However Price Action is not normally distributed and thus can not be conventionally interpreted in this way, Formally the Fisher Transform, transforms the distribution of bounded ranging price action (were price action takes values in a range from -1 to 1) into that of a normal distribution, alternatively it may be said the Fisher Transform changes the PDF of any waveform so that the transformed output has n approximately Gaussian PDF, It does so through the following equations. taken directly from the work of John F. Ehlers - Using The Fisher Transform

By substituting price data in the above formulas, bounded ranging price actions (over a given user defined period lookback - this determines the range price ranges in, see the Intermediate formula above) distribution is transformed to that in the normal case. This means when the input, the Intermediate ,(the Midpoint - see formula above) approaches either limit within the range the outputs are greatly amplified, this amplification accentuates /puts more weight on the larger deviations or limits within the range, conversely when price action is varying round the mean of the range the output is approximately equal to unity (the input is approximately equal to the input, the intermediate)

The inputs (Intermediates) are converted to normal outputs and the nonlinear Transfer of the Fisher Transform with varying senesitivity's (gammas) can be seen in the graph / image above. Although sensitivity adjustments are not currently available in this script (I forgot to add it) the outputs may be greatly amplified as gamma (the coefficient of the Fisher Transformation - see Fish equation) approaches 1. the purple line show this graphically, as a higher gamma leads to a greater amplification than in the standard case (the red line which is the standard fisher transformation, the black plot is the Fish with a gamma of 1, which is unity sensativity)

Reversal plots and Breakouts :

- Support lines are plotted with their corresponding Fish value when there is a crossover of the Fish and Fish SMA <= a given standard deviation of Fish

- Resistance lines are plotted with their corresponding Fish value when there is a crossunder of the Fish and Fish SMA >= a given standard deviation of Fish

- Reversals are these support and resistance line plots

Breakouts and Volume bars :

Breakouts cause the reversal lines to break (when the high/low is above the resistance/support), Breakouts are more "high quality" when they occur conditional on high volume, the highlighted bars represent volume standard deviations ranging from -3 to 3. When breakouts occure on high volume this may be a sign of the continutaion of the trend (reversals would signify the start of a new trend).

Hope you enjoy, Happy Trading !
(be sure to rocket the script if you liked it, this helps me know which of my scripts are the most useful)

เอกสารเผยแพร่:
FTR V2

- Fisher support and Resistance Line Extend option, this may be useful to identify the validity of these reversal or continuation points as support and resistance zones.

- Max Lines Options, this helps to make the chart less cluttered, only plotting the quantity of lines equal to the quantity specified (default being 20)

- Fisher Support and Resistance lines width option, This allows for the user to adjust the line plots width for more clearer visualization.

The above plot shows the FTR with all V2 updates

As always, If you would like any updates to the script please let me know in the commoners, this way the utility of all indicators can be improved, its called collective innovation !.
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