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### Fisher Center of Gravity Oscillator

This study calculates and displays a Fisher Center of Gravity Oscillator and Trigger Line for the data given by the **Input Data** Input. This study is an ACSIL implementation of the Indicator given in Figures 8.13 and 8.14 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 \(n\).

We begin by computing the Stochastic Center of Gravity Oscillator, \(CG^{(Stoch)}_t(X,n)\).

Next we denote the **Fisher Center of Gravity Oscillator** at Index \(t\) as \(CG^{(Fish)}_t(X,n)\).

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

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

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

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

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

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

\(Trig_t^{(FCG)}(X,n) = CG^{(Fish)}_{t - 1}(X,n)\)#### 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.

#### Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through **File >> Open Spreadsheet**.

*Last modified Sunday, 21st November, 2021.