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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.