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## Moving Average - Triple Exponential

This study calculates and displays a Triple Exponential Moving Average of the data specified by the **Input Data** Input.

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 \(n\). Then we denote the **Moving Average - Triple Exponential** at Index \(t\) for the given Inputs as \(TEMA_t(X,n)\), and we compute it using the following sequence of Exponential Moving Averages for the given Inputs.

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

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

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 \(TEMA_t(X,n)\) in terms of these **Exponential Moving Averages** for \(t \geq n\) as follows.

#### Inputs

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*Last modified Wednesday, 03rd January, 2018.