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### Stochastic Cyber Cycle

This study calculates and displays a Stochastic Cyber Cycle and Trigger Line for the data given by the **Input Data** Input. This study is an ACSIL implementation of the Indicator given in Figures 8.4 and 8.5 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 Ratio of the Cyber Cycle, \(StochRat_t(CC(X,n),n)\).

Then we compute a smoothed Stochastic Ratio, denoted as \(StochRat_t^{(S)}(CC(X,n),n)\), which we compute as follows.

\(\displaystyle{StochRat_t^{(S)}(CC(X,n),n) = \frac{1}{10}\sum_{j = 1}^4 j \cdot StochRat_{t - 4 + j}(CC(X,n),n)}\)We then compute the **Stochastic Cyber Cycle**, denoted as \(CC^{(Stoch)}_t(X,n)\), as follows.

The Trigger Line for this Indicator is given below.

\(Trig^{(SCC)}_t(X,n) = 0.96\left(CC^{(Stoch)}_{t - 1}(X,n) + 0.02\right)\)#### 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 Tuesday, 26th July, 2022.