# Technical Studies Reference

### Moving Average - Hull

This study calculates and displays a Hull Moving Average of the data specified by the Input Data Input. This moving average was developed by Alan Hull.

Let $$X$$ be a random variable denoting the Input Data, and let the Input Hull Moving Average Length be denoted as $$n$$. Let $$WMA\left(X,\left\lfloor{\frac{n}{2}}\right\rfloor\right)$$ and $$WMA(X,n)$$ be random variables denoting the Weighted Moving Averages for $$X$$ with Lengths $$\left\lfloor{\frac{n}{2}}\right\rfloor$$ and $$n$$, respectively. Then we denote the Moving Average - Hull at Index $$t$$ for the given Inputs as $$HMA_t(X,n)$$, and we compute it for $$t \geq n + \left\lfloor{\sqrt{n} + \frac{1}{2}}\right\rfloor - 1$$ as follows.

$$HMA_t(X,n) = WMA_t\left(2WMA\left(X, \left\lfloor{\frac{n}{2}}\right\rfloor\right) - WMA(X,n), \left\lfloor{\sqrt{n}+\frac{1}{2}}\right\rfloor\right)$$

For an explanation of the floor function ($$\left\lfloor{\space\space}\right\rfloor$$), refer to our description here.