# Technical Studies Reference

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# T3

This study calculates and displays a T3 Moving Average of the data specified by the **Input Data** Input. The study was developed by Tim Tillson.

Let \(X\) be a random variable denoting the **Input Data**, and let \(X_t\) be the value of the **Input Data** at Index \(t\). Let the Input **Length** be denoted as \(n\), and let the Input **Multiplier** be denoted as \(v\). Then we denote the value of **T3** at Index \(t\) for the given Inputs as \(T3_t(X,n,v)\), and we compute it using the following sequence of Exponential Moving Averages for the given Inputs.

\(EMA_t^{(2)}(X,n) = EMA_t(EMA(X,n),n)\)

\(EMA_t^{(3)}(X,n) = EMA_t(EMA(EMA(X,n),n),n)\)

\(EMA_t^{(4)}(X,n) = EMA_t(EMA(EMA(EMA(X,n),n),n),n)\)

\(EMA_t^{(5)}(X,n) = EMA_t(EMA(EMA(EMA(EMA(X,n),n),n),n),n)\)

\(EMA_t^{(6)}(X,n) = EMA_t(EMA(EMA(EMA(EMA(EMA(X,n),n),n),n),n),n)\)

In the above relations, \(EMA_t^{(j)}\) denotes the \(j-\)fold composition of the \(EMA\) function with itself, and \(EMA(X,n)\) is a random variable denoting the **Exponential Moving Average** of **Length** \(n\) for the **Input Data** \(X\). We compute \(T3_t(X,n,v)\) in terms of these **Exponential Moving Averages** for \(t > 0\) 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 Monday, 03rd October, 2022.