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# 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 $$n_t^{(NZ)}$$. 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.

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

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

#### Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

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*Last modified Tuesday, 19th March, 2019.