# 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.