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Technical Studies Reference

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.

\(EMA_t^{(1)}(X,n) = EMA_t(X,n)\)
\(EMA_t^{(2)}(X,n) = EMA_t(EMA(X,n),n)\)
\(EMA_t^{(3)}(X,n) = EMA_t(EMA(EMA(X,n),n),n)\)

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.

\(TEMA_t(X,n) = 3EMA_t^{(1)}(X,n) - 3EMA_t^{(2)}(X,n) + EMA_t^{(3)}(X,n)\)


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*Last modified Tuesday, 27th September, 2022.