# Technical Studies Reference

### Vortex

This study calculates and displays two Vortex Indicators of the Price Data.

Let $$H_t$$, $$L_t$$, and $$C_t$$ be the values of the High, Low, and Close Prices, respectively, at Index $$t$$. Let the Input Vortex Length be denoted as $$n$$.

We begin by computing the True Range, as well as two other quantities called the Vortex Movement - Up and Vortex Movement - Down. These values of the latter two quantities at Index $$t$$ are denoted as $$VM^{(Up)}_t$$ and $$VM^{(Down)}_t$$, respectively. We compute them as follows.

$$\displaystyle{VM^{(Up)}_t = \left\{ \begin{matrix} |H_0 - L_0| & t = 0 \\ |H_t - L_{t - 1}| & t > 0 \end{matrix}\right .}$$

$$\displaystyle{VM^{(Down)}_t = \left\{ \begin{matrix} |L_0 - H_0| & t = 0 \\ |L_t - H_{t - 1}| & t > 0 \end{matrix}\right .}$$

We then compute the two Vortex Indicators, denoted $$VI^{(+)}_t(n)$$ and $$VI^{(-)}_t(n)$$, as follows.

$$\displaystyle{VI^{(+)}_t(n) = \left\{ \begin{matrix} \Sigma_{i = 0}^t VM^{(Up)}_t / \Sigma_{i = 0}^t TR_t & t < n - 1 \\ \Sigma_{i = t - n + 1}^t VM^{(Up)}_t / \Sigma_{i = t - n + 1}^t TR_t & t \geq n - 1 \end{matrix}\right .}$$

$$\displaystyle{VI^{(-)}_t(n) = \left\{ \begin{matrix} \Sigma_{i = 0}^t VM^{(Down)}_t / \Sigma_{i = 0}^t TR_t & t < n - 1 \\ \Sigma_{i = t - n + 1}^t VM^{(Down)}_t / \Sigma_{i = t - n + 1}^t TR_t & t \geq n - 1 \end{matrix}\right .}$$

These formulas hold provided that the denominators are nonzero.

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