# Technical Studies Reference

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### Cyber Cycle

This study calculates and displays a 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 4.2 and 4.6 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** and **Lag** Inputs be denoted as \(n\) and \(\ell\), respectively.

We first smooth the data using a Four Bar Symmetrical Finite Impulse Response Filter. The value of the smoothed data at Index \(t\) is denoted as \(X^{(S)}_t\), and we compute it as follows.

\(\displaystyle{X^{(S)}_t = \frac{1}{6}(X_t + 2X_{t - 1} + 2X_{t - 2} + X_{t - 3})}\)We compute two Smoothing Factors \(\alpha(n)\) and \(\beta(\ell)\) (Greek letters alpha and beta, respectively) as follows.

\(\displaystyle{\alpha(n) = \frac{2}{n + 1}}\)\(\displaystyle{\beta(\ell) = \frac{1}{\ell + 1}}\)

We will suppress the functional dependence of \(\alpha\) and \(\beta\) on \(n\) and \(\ell\), respectively, in the following formulas.

The **Cyber Cycle** and the Trigger Line at Index \(t\) are denoted as \(CC_t(X,n)\) and \(Trig^{(CC)}_t(X,n,\ell)\), respectively. Both of these are displayed as Subgraphs, and we compute them as follows.

\(Trig^{(CC)}_t(X,n,\ell) = \beta CC_t(X,n) + (1 - \beta)Trig^{(CC)}_{t - 1}(X,n,\ell)\)

#### 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 Monday, 22nd November, 2021.