**Excerpt of my latest article in the October 2010 S&C magazine**

The Fisher transform has been a familiar concept to STOCKS & COMMODITIES readers in recent years following its introduction in 2002 by frequent S&C contributor John Ehlers. Its creator, Ronald Fisher, was one of the leading scientists of the 20th century, making major contributions to statistics, evolutionary biology, and genetics. Ehlers' 2004 followup index (RSI), changing what was a good turning-point indicator to one that fine-tuned the timing of possible entry and exit points. Here is the inverse Fisher transform formula:

y = (Exp(2 * x) - 1)/(Exp(2 * x) + 1)

where x is the input value and y is the transformed value. Figure 1 shows a plot of the inverse Fisher transform. The transform creates boundaries to keep the output value in the range between -1 to +1. Input values larger than 2 generate a result close to 1, while input values less than -2 generate a result close to -1. This boundary characteristic is useful with

any indicator moving between two fixed values, like the relative strength index (RSI).

But the input data for the inverse Fisher transform formula needs to be in the range of -5 to +5. The normal RSI is in the range of zero to 100, but we can convert this to a range of -5

to 5, using the following formula:

x = 0.1 * (RSI value - 50)

FIGURE 1: INVERSE FISHER TRANSFORM. The transform creates boundaries to keep the output value in the range of -1 to +1. Input values larger than 2 generate a result close to 1, and input values less than -2 generate a result close to -1. This boundary characteristic is useful with any indicator moving between two fixed values, like the RSI.

**RSI to Inverse Fisher Transform**

With the inverse Fisher transform RSI values above 60 will be squeezed into the top 12% of the range, and RSI values below 40 will be squeezed into the bottom 12% of the range. The transform causes the RSI transition from 40 to 60, to be plotted as a very sharp swing. In Figure 3 you see a chart starting with a flat price move, followed by an up and down price move. You can compare the original RSI in blue with its inverse Fisher transform in red (first and second graphs below the price plot). In his 2004 article, John Ehlers used a nine-day weighted moving average on the inverse Fisher transform with a five day RSI to create clearer buy and sell points. This is the green curve in Figure 2 (the third graph below the price plot). When the curve crosses above 27, it is a buying point, and when it falls below 73, it is a selling point. What I want to achieve is the last black curve that you can see on the bottom pane. If you compare this curve with the green one, you will see that you generally get faster buy and sell signals with very clear turning points reaching the zero and 100 level.

FIGURE 2: RSI TO SVE INVERSE FISHER RSI. Here you see the RSI, inverse Fisher transform, John Ehlers' inverse Fisher transform, and the SVE inverse Fisher RSI. Which one gives you faster buy and sell signals with clear turning points?

Look for the formula and learn how to trade with this indicator reading the complete article in the October 2010 issue of Stocks & Commodities magazine.

Sylvain Vervoort http://stocata.org/

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