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.

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.