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Technical Studies Reference


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.

\(\displaystyle{X^{(Fish)}_t(n) = \frac{1}{2}\ln\left|\frac{1 + 1.98(X^{(Stoch)}_t(n) - 0.5)}{1 - 1.98(X^{(Stoch)}_t(n) - 0.5)}\right|}\)

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.

\(\displaystyle{X^{(Fish)}_t(n) = \frac{1}{2}\ln\left(\frac{1 + 1.98(X^{(Stoch)}_t(n) - 0.5)}{1 - 1.98(X^{(Stoch)}_t(n) - 0.5)}\right)}\)

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.