# 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):

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

## Examples of Fisher Transform

- In trading, the Fisher Transform indicator is used to identify potential trend reversals. It is created by applying a mathematical transformation to the price data to create a Gaussian probability distribution. The resulting signal shows clear turning points, which can be used to identify possible entry or exit points in the market.
- In a manufacturing environment, the Fisher Transform can be used to identify process variability. By applying a Fisher Transform to process data, outliers can be identified and corrective action can be taken to ensure the process is running smoothly and efficiently.
- In the medical field, the Fisher Transform can be used to detect anomalies in patient data. By applying the transform to patient data, doctors can quickly identify any abnormal readings and take appropriate action to ensure the patient's health and safety.

## Advantages of Fisher Transform

The Fisher Transform is a useful tool for identifying trend reversals in any financial instrument. The main advantages of this indicator are as follows:

- It provides more precise, sharper turning points than other momentum-class indicators. This makes it easier to identify trend reversals.
- It transforms the distribution of price changes into a normal (Gaussian) distribution, making it easier to analyze the data.
- It is easy to implement and can be used for any financial instrument.
- It is a reliable indicator that can be used in combination with other technical analysis tools.
- It is a useful tool for traders as it helps to identify potential entry and exit points.

## Limitations of Fisher Transform

The Fisher Transform has its own limitations, which should be taken into account when using it for trading:

- The Fisher Transform is not suitable for charting the most price movements, as it takes a lot of time to generate a signal.
- It is necessary to use a filter to reduce the noise in the generated signals, otherwise it could lead to false signals.
- The Fisher Transform is not suitable for short-term trading, because it takes a lot of time to generate a signal.
- The Fisher Transform is sensitive to the choice of parameters, which can lead to false signals.
- The Fisher Transform is not suitable for long-term trends, as its signals tend to be short-term in nature.
- The Fisher Transform is not suitable for identifying dynamic support and resistance levels, as its signals are not always reliable.

There are several other approaches related to Fisher Transform which are used to identify trend reversals.

**The Relative Strength Index (RSI)**: This is a momentum-based indicator which measures the magnitude of recent price changes to measure speed and direction of a trend. It is calculated by comparing the magnitude of recent gains and losses over a specified time frame and then normalizing the results.**The Moving Average Convergence/Divergence (MACD)**: This is a momentum indicator which uses the difference between two moving averages to identify trend strength and direction. The MACD is calculated by subtracting a longer period EMA from a shorter period EMA.**The Stochastic Oscillator**: This is a momentum indicator which is used to identify potential trend reversals. It is calculated by taking the current closing price and comparing it to the range of prices over a specified period of time.**The Average Directional Index (ADX)**: This is a trend-following indicator which uses the difference between two moving averages to measure the strength of a trend. The ADX is calculated by taking the difference between two EMAs and then normalizing the result.

In summary, the Fisher Transform is an indicator that can be used to identify trend reversals. It is often used in conjunction with other approaches such as the Relative Strength Index (RSI), Moving Average Convergence/Divergence (MACD), Stochastic Oscillator, and Average Directional Index (ADX) to provide more precise and sharper turning points.

## 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