# Technical Studies Reference

### Moving Average - Welles Wilders

This study calculates and displays a Welles Wilders Moving Average of the data specified by the Input Data Input.

Let $$X$$ be a random variable denoting the Input Data, and let $$X_t$$ be the value of the Input Data at Index $$t$$. Let the Input Length be denoted as $$n$$. Then we denote the Moving Average - Welles Wilders at Index $$t$$ for the given Inputs as $$WWMA_t(X,n)$$, and we compute it using the following recursion relation.

For $$t = 0$$: $$WWMA_0 = X_0$$

For $$t > 0$$: $$WWMA_t(X,n) =\left\{ \begin{matrix} SZMA_t(X,n) & WMMA_{t-1}(X,n) = 0 \\ WWMA_{t-1}(X,n) + \frac{1}{n}\left(X_t - WWMA_{t-1}(X,n)\right) & WWMA_{t-1}(X,n) \neq 0 \end{matrix}\right .$$

In the above function, $$SZMA_t(X,n)$$ refers to Moving Average - Simple Skip Zeros.