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### Moving Average - Triangular

This study calculates and displays a Triangular Moving Average of the data specified by the **Input Data** Input. The Triangular Moving Average is calculated in terms of the Simple Moving Average. Refer to that study to familiarize yourself with the notation used here.

Just as with the Simple Moving Average, this study relies on the Inputs **Data Input** \(X\) and **Length** \(n\). We calculate two additional **Lengths** based on \(n\), \(n_1(n)\) and \(n_2(n)\), as follows.

\(\displaystyle{n_2(n) =\left\{ \begin{matrix} \left\lceil{\frac{n}{2}}\right\rceil & n \space odd\\ n_1 + 1 & n \space even \end{matrix}\right .}\)

For an explanation of the ceiling function (\(\left\lceil{\space\space}\right\rceil\)), refer to our description here.

We denote the **Moving Average - Triangular** at Index \(t\) for the given **Input Data** and calculated **Lengths** as \(TMA_t(X,n)\), and we compute it for \(t \geq n_1(n) + n_2(n) - 1\) as follows.

#### 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 Friday, 14th June, 2019.