Fisher Transform - Technical Indicator

In the November 2002 issue of the Stocks and Commodities magazine, John Ehlers wrote an article "Using the Fisher Transform" and introduced a technical analysis indicator called the Fisher Transform or Fish.
Fisher Transform indicator is used to identify price reversals and is based on the assumption that prices behave like a square wave and do not follow a Gaussian or normal distribution. In fact, a Gaussian probability density function (PDF) is a bell-shaped curve where 68% of the samples are within one standard deviation from the mean; this is clearly not true.

The fisher transform formula transforms the probability density function of any waveform to a function that has almost a Gaussian PDF.

The function can transform stock or instrument prices as well as any technical indicator. For example you can apply the fisher transform to the relative strength index indicator. The transformed time series has very sharp turning points and therefore produce clear and precise bullish and bearish signals. It can be applied to Forex currencies, stocks or ETFs.

The indicator accepts a time series as a first parameter and a period as a second parameter.
Example:
f = Fisher((high + low) / 2, 10);




Bullish and bearish signals occur when the Fisher line crosses above or below its signal line, which is the fisher transform one bar ago.
Here is the formula of the fisher signal line:
f = Fisher((high + low) / 2, 10);
signal = ref(f, 1);

Here is a way to generate trading signals using the fisher transform indicator:
A bullish signal is generated when the fisher line turns up below -1 threshold and crosses above the signal line.
A bearish signal is generated when the fisher line turns down above the 1 threshold and crosses below the signal line.

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