# Fisher Transform

Fisher Transform | |
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**The Fisher transform** is an indicator that identifies trend reversals. This oscillator can be successfully used for any financial instruments. This instrument was founded by J. F. Ehlers and aims to transform the distribution of price changes into a normal (Gaussian) distribution. The sign values swing around the zero line forming clear turning points, which simplifies the classification of trend reversals. This indicator is widely used as part of a trading procedure based on price action and is rather not used alone. **The Fisher Transform** is an uncomplicated analytical process used to transform any data set into a transformed data set whose Probability Density Function (PDF) is generally Gaussian (J.F.Ehlers 2011, p.2). The Fisher Transform provides more precise, sharper turning points than a regular momentum-class sign (Wiley 2017,p.441). The **mission of the Fisher Transform** is to take any sign possessing a nominally zero mean and bounced among the limits of -1 to +1 and transform the amplitude so that the modified indicator has an estimated natural possibility distribution (J.F.Ehlers 2013,p.195).

## The formula of the Fisher Transform

The Fisher Transform converts the Probability Density Function (PDF) of any waveform so that the converted output has a generally Gaussian PDF. The formula of the **Fisher Transform** is presented as (J.F.Ehlers 2011,p.3):

**\(y=0.5*ln\frac{1\,+\,x}{1\,-\,x}\)**

- x = the input
- y = the output
- ln = the natural logarithm

## The Inverse of the Fisher Transform

**The Inverse Fisher Transform** is perfect for forming a pointer that presents clear buy and sells signs in the cause of bipolar possibility delivery. This formula is discovered by solving comparison 1 for x in terms of y. The formula of the Inverse Fisher Transform is compressive and it is shown as (J.Ehlers 2004, p.1):

**\(x=\frac{e^{2y}\,-\,1}{e^{2y}\,+\,1}\)**

## References

- Ehlers J., (2004),
*The Inverse Fisher Transform by John Ehlers*,"Technical Analysis of Stocks and Commodities", No.22, p.1 - Ehlers F.J., (2002),
*Using The Fisher Transform*, "Technical Analysis of Stocks and Commodities", No.20, p.1-3 - Ehlers F.J., (2011),
*Cybernetic Analysis for Stocks and Futures: Cutting-Edge DSP Technology to Improve Your Trading*, John Wiley & Sons, New Jersey - Ehlers F.J., (2013),
*Cycle Analytics for Traders: Advanced Technical Trading Concepts*, John Wiley & Sons, New Jersey - Hunter E.J., Schmidt L.F., (2004),
*Methods of Meta-Analysis: Correcting Error and Bias in Research Findings*, SAGE, United States of America - Kaufman J.P., (2013),
*Trading Systems and Methods*, John Wiley & Sons, New Jersey - Mielke W.P., Berry J.K., (2007),
*Permutation Methods: A Distance Function Approach*, Springer Science & Business Media, New York - Wiley, (2017),
*CMT Level II 2018: Theory and Analysis*, John Wiley & Sons, New Jersey

**Author:** Paulina Zając