# Technical Studies Reference

## Moving Average - Simple Skip Zeros

This study calculates and displays a Simple Moving Average of the data specified by the Input Data Input, excluding the values that are equal to zero.

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 Input Length be denoted as $$n$$, and let the number of nonzero values of $$X$$ from $$X_{t-n+1}$$ through $$X_t$$ be denoted as $$n_{NZ}$$. Then we denote the Moving Average - Simple Skip Zeros at Index $$t$$ for the given Inputs as $$SZMA_t(X,n)$$, and we compute it for $$t \geq n - 1$$ as follows.

$$\displaystyle{SZMA_t(X,n) =\left\{ \begin{matrix} \left. \left(\sum_{i = t - n + 1}^tX_i\right) \middle/ n_{NZ}\right. & n_{NZ} \neq 0 \\ 0 & n_{NZ} = 0 \end{matrix}\right .}$$

For an explanation of the Sigma ($$\Sigma$$) notation for summation, refer to our description here.