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### Instantaneous Trendline

This study calculates and displays an Instantaneous Trendline and Trigger Line for the data given by the **Input Data** Input. This study is an ACSIL implementation of the ITrend Indicator given in Figure 3.4 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 compute a Smoothing Factor \(\alpha(n)\) (Greek letter alpha) as follows.

\(\displaystyle{\alpha(n) = \frac{2}{n + 1}}\)We will suppress the functional dependence of \(\alpha\) on \(n\) in the following formulas.

The **Instantaneous Trendline** and the Trigger Line at Index \(t\) are denoted as \(IT_t(X,n)\) and \(Trig^{(IT)}_t(X,n)\), respectively. Both of these are displayed as Subgraphs, and we compute them as follows.

\(Trig^{(IT)}_t(X,n) = 2IT_t(X,n) - IT_{t - 2}(X,n)\)

#### 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 Thursday, 02nd September, 2021.