# Technical Studies Reference

### Rate of Change - Percentage

This study calculates and displays the Percent Change of the data specified by the Input Data Input over a period specified by the Length 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 Inputs Length and Multiplication Factor be denoted as $$n$$ and $$v$$, respectively. Then we denote the Rate of Change - Percentage at Index $$t$$ for the given Inputs as $$\%Diff_t(X,n,v)$$, and we compute it for $$t \geq n$$ as follows.

$$\displaystyle{\%Diff_t(X,n,v) = \frac{X_t - X_{t - n}}{X_{t - n}}\cdot v}$$

This study displays a true Percent Change only if $$v = 100$$.