# Technical Studies Reference

- Technical Studies Reference
- Common Study Inputs (Opens a new page)
- Using Studies (Opens a new page)

### RSI - TS

This study calculates and displays Tradestation's implementation of the RSI.

Let \(X\) be a random variable denoting the **Input Data** Input, and let \(X_t\) be the value of the **Input Data** at Index \(t\). Let the Inputs **RSI Length** and **RSI Moving Average Length** be denoted as \(n_{RSI}\) and \(n_\overline{RSI}\), respectively.

We begin by calculating the Net Change Average and the Total Change Average, whose respective values at Index \(t\) are denoted as \(NCA_t(X,n_{RSI})\) and \(TCA_t(X,n_{RSI})\). We compute these for \(t \geq n_{RSI}\) as follows.

\(\displaystyle{NCA_t(X,n_{RSI}) =\left\{ \begin{matrix} \frac{1}{n_{RSI}}(X_t - X_{t - n_{RSI}}) & t = n_{RSI} \\ NCA_{t - 1} + \frac{1}{n_{RSI}}(X_t - X_{t - 1} - NCA_{t - 1}) & t > n_{RSI} \end{matrix}\right .}\)\(\displaystyle{TCA_t(X,n_{RSI}) =\left\{ \begin{matrix} \frac{1}{n_{RSI}} \Sigma_{i = 1}^t |X_i - X_{i - 1}| & t = n_{RSI} \\ TCA_{t - 1} + \frac{1}{n_{RSI}}(|X_t - X_{t - 1}| - TCA_{t - 1}) & t > n_{RSI} \end{matrix}\right .}\)

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

The **Relative Strength Index - TS** at Index \(t\) is denoted as \(RSI^{(TS)}_t(X,n_{RSI})\), and it is computed for \(t \geq n_{RSI}\) as follows.

The Moving Average of \(RSI^{(TS)}_t\left(X,n_{RSI}\right)\) at Index \(t\) is denoted as \(\overline{RSI}_t(X,n_{RSI},n_{\overline{RSI}})\). This Moving Average is calculated for \(t \geq n_{RSI} + n_{\overline{RSI}}\) as follows.

\(\overline{RSI}_t(X,n_{RSI},n_{\overline{RSI}}) = SMA_t(RSI(X,n_{RSI}),n_{\overline{RSI}})\)In the above formula, \(SMA\) denotes the Simple Moving Average.

#### Inputs

#### Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through **File >> Open Spreadsheet**.

*Last modified Thursday, 16th September, 2021.