# Technical Studies Reference

### Coppock Curve

This study calculates and displays a Coppock Curve for the data specified by the Input Data Input.

Let $$X$$ be a random variable denoting the Input Data, and let $$X_t$$ be its value at Index $$t$$. Let $$n$$ be the Moving Average Length Input. We introduce two Rate of Change Oscillators, denoted as $$ROC_t(X,14,100)$$ and $$ROC_t(X,11,100)$$. The notation is taken from the Rate of Change - Percentage study. We compute these oscillators for $$t \geq 0$$ as follows.

$$\displaystyle{ROC_t(X,14,100) =\left\{ \begin{matrix} 100\cdot\frac{X_t - X_0}{X_0} & t \leq 14 \\ 100\cdot\frac{X_t - X_{14}}{X_{14}} & t > 14 \end{matrix}\right .}$$

$$\displaystyle{ROC_t(X,11,100) =\left\{ \begin{matrix} 100\cdot\frac{X_t - X_0}{X_0} & t \leq 11 \\ 100\cdot\frac{X_t - X_{11}}{X_{11}} & t > 11 \end{matrix}\right .}$$

We denote the value of the Coppock Curve at Index $$t$$ as $$CC_t(X,n)$$, and we compute it for $$t \geq 0$$ in terms of a Weighted Moving Average as follows.

$$CC_t(X,n) = WMA_t\left(ROC(X,14,100) + ROC(X,11,100), n\right)$$