# Technical Studies Reference

- Technical Studies Reference
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### RSI

This study calculates the Welles Wilder Relative Strength Index (RSI) of the data specified by the **Input Data** Input. The study also calculates a Moving Average of the RSI. It displays graphs of both of these functions, in addition to two horiztonal lines, which are specified by the Inputs **Line1 Value** and **Line2 Value**. Both the RSI and the Moving Average of the RSI have an associated **Length** Input: **RSI Length** \(n_{RSI}\) and **RSI Moving Average Length** \(n\), respectively.

Let \(X\) be a random variable denoting the **Input Data**, and let \(X_t\) be the value of the **Input Data** at Index \(t\). Then we denote the Upward Change and Downward Change in \(X\) at Index \(t\) as \(U_t(X)\) and \(D_t(X)\), respectively. We compute these for \(t > 0\) as follows.

\(\displaystyle{D_t(X) =\left\{ \begin{matrix} 0 & X_t > X_{t - 1} \\ X_{t - 1} - X_t & X_t \leq X_{t - 1} \end{matrix}\right .}\)

The **Relative Strength Index** at Index \(t\) is denoted as \(RSI_t\left(X,n_{RSI}\right)\), and it is computed for \(t \geq n_{RSI} + n\) as follows.

In the above formula, \(U(X)\) and \(D(X)\) are random variables denoting the Upward and Downward Changes in \(X\), respectively.

**Note**: For the purposes of computing \(RSI_t\left(X,n_{RSI}\right)\) for \(t \geq n_{RSI} + n\), we use internal calculations for \(n_{RSI} - 1 \leq t < n_{RSI} + n\) using the last formula given above. These values are not returned as output.

The Moving Average of \(RSI_t\left(X,n_{RSI}\right)\) with Length **RSI Moving Average Length** \(n\) at Index \(t\) is denoted as \(\overline{RSI}_t(X,n_{RSI},n)\). This Moving Average is calculated in terms of a Simple Moving Average for \(t \geq n_{RSI} + n\) as follows.

In the above formula, \(RSI(X,n_{RSI})\) is a random variable denoting the RSI of \(X\) with **Length** \(n\).

**Note**: For the purposes of computing \(\overline{RSI}_t(X,n_{RSI},n)\) for \(t \geq n_{RSI} + n\), we use internal calculations for \(n_{RSI} +n - 2 \leq t < n_{RSI} + n\) using the last formula given above. These values are not returned as output.

**Note**: Depending on the setting of the Input **Average Type**, the Simple Moving Averages in the calculations of \(RS_t\left(X,n_{RSI}\right)\) and \(\overline{RSI}_t(RSI(X,n_{RSI}),n)\) could be replaced with Exponential Moving Averages, Linear Regression Moving Averages, Weighted Moving Averages, Wilders Moving Averages, Simple Moving Averages - Skip Zeros, or Smoothed Moving Averages. The types of all three Moving Averages in the calculation are determined by this one Input.

#### 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 Tuesday, 26th June, 2018.