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# Center of Gravity Oscillator

### Description

This study calculates and displays a 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 5.1 and 5.2 of the book *Cybernetic Analysis for Stocks and Futures* by John Ehlers.

Let \(X\) be a random variable denoting the **Input Data**, and let \(X_t\) be the value of \(X\) at Index \(t)\. Let the **Length** Input be denoted as \(n\).

We denote the values of the **Center of Gravity Oscillator** and the Trigger Line for the given Inputs at Index \(t\) as \(CG_t(X,n)\) and \(Trig^{(CG)}_t(X,n)\), respectively, and we compute them as follows.

\(Trig^{(CG)}_t(X,n) = CG_{t - 1}(X,n)\)

For an explanation of the Sigma (\(\Sigma\)) notation for summation, refer to our description here.

#### Inputs

#### 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 Wednesday, 01st February, 2023.