# Technical Studies Reference

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### 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.

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

These formulas hold provided that the denominators are nonzero.

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

#### Inputs

#### Spreadsheet

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*Last modified Thursday, 02nd September, 2021.