Technical Studies Reference

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.

\(SMMA_0(X,n) = 0\)
\(\displaystyle{SMMA_t(X,n) = \left. \left(\sum_{i=t-n}^{t-1}X_i - SMMA_{t-1}(X,n) + X_t\right) \middle/ n\right.}\)

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


  • 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.