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### Moving Average - Smoothed

This study calculates 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 chart bar \(i\). Let the Input **Length** be denoted as \(n\). Then we denote the **Moving Average - Smoothed** at chart bar \(t\) for the given Inputs as \(SMMA_t(X,n)\), and we compute it with the following recursion relation.

\(\displaystyle{SMMA_t(X,n) = \left. \left(\sum_{i=t-n}^{t-1}X_i - SMMA_{t-1}(X,n) + X_t\right) \middle/ n\right.}\)

For an explanation of the Sigma (\(\Sigma\)) notation for summation, refer to the Wikipedia article Summation.

#### Inputs

- Input Data
- Length
**Offset**: This Input specifies the number of chart bars by which the summation index is to be shifted to the left.

*Last modified Friday, 09th June, 2017.