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# Fisher Function

This study calculates and displays a Fisher Function and Trigger Line for the data given by the **Input Data** Input. This study is an ACSIL implementation of the Fisher functions described Chapter 8 of the book *Cybernetic Analysis for Stocks and Futures* by John Ehlers.

Let \(X\) be a random variable denoting the **Input Data**, and let the **Length** Input be denoted as \(n\).

**Note**: This study is not meant to be applied to Price Data. It is meant to be applied to an oscillator.

To apply the Fisher Function, take the following steps.

- Add the desired oscillator study to a chart.
- Add the Fisher Function study to a chart.
- Select the Fisher Function study in the
**Studies to Graph**section of the**Chart Studies**window and click**Settings**. - In the
**Study Settings**window for the Fisher Function, go to**Based On**and select the oscillator. - For the
**Input Value**of the**Input Data**, select the Subgraph corresponding to the oscillator. - In the
**Study Settings**window, click OK. - In the
**Chart Studies**window, click OK.

We begin by computing the Stochastic Function for the oscillator, \(X^{(Stoch)}_t(n)\).

Next we denote the **Fisher Function** at Index \(t\) as \(X^{(Fish)}_t(n)\).

If the **Use Absolute Value When Log Argument Is Zero** Input is set to Yes, then we compute \(X^{(Fish)}_t(n)\) as follows.

This formula is used under the conditions \(\frac{1 + 1.98(X^{(Stoch)}_t(n) - 0.5)}{1 - 1.98(X^{(Stoch)}_t(n) - 0.5)} \neq 0\) and \(1 - 1.98(X^{(Stoch)}_t(n) - 0.5) \neq 0\). Otherwise, \(X^{(Fish)}_t(n) = 0\).

If the **Use Absolute Value When Log Argument Is Zero** Input is set to No, then we compute \(X^{(Fish)}_t(n)\) as follows.

This formula is used under the conditions \(\frac{1 + 1.98(X^{(Stoch)}_t(n) - 0.5)}{1 - 1.98(X^{(Stoch)}_t(n) - 0.5)} > 0\) and \(1 - 1.98(X^{(Stoch)}_t(n) - 0.5) \neq 0\). Otherwise, \(X^{(Fish)}_t(n) = 0\).

**Note**: For an explanation of the Logarithmic Function (\(\ln()\)), see the documentation here.

The Trigger Line is denoted as \(Trig_t^{(FX)}(n)\), and is computed as follows.

\(Trig_t^{(FX)}(n) = X^{(Fish)}_{t - 1}(n)\)#### Inputs

- Input Data
- Length
**Use Absolute Value When Log Argument Is Zero**: This custom Input determines the method of calculation of the Fisher Center of Gravity Oscillator, as described above.

*Last modified Monday, 26th September, 2022.