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Technical Studies Reference

Moving Average - Smoothed

This study calculates and displays a smoothed moving average of the data specified by the Input Data Input.

Let \(X\) be a random variable denoting the Input Data, and let \(X_i\) be the value of the Input Data at Index \(i\). Let the Length Input be denoted as \(n\). Then we denote the Moving Average - Smoothed at Index \(t\) for the given Inputs as \(SMMA_t(X,n)\), and we compute it for \(t \geq n - 1\) as follows.

\(\displaystyle{SMMA_t(X,n) = \left\{\begin{matrix} SMA_{n - 1}(X,n) & t = n - 1 \\ \frac{n\cdot SMMA_{t - 1}(X,n) - SMMA_{t - 1}(X,n) + X_t}{n} & t > n - 1 \end{matrix}\right .}\)

In the above formula, \(SMA_{n - 1}(X,n)\) denotes the Simple Moving Average at \(t = n - 1\).



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*Last modified Tuesday, 27th September, 2022.