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Technical Studies Reference


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.

\(\displaystyle{RSI^{(TS)}_t(X,n_{RSI}) =\left\{ \begin{matrix} 50\left(\frac{NCA_t(X,n_{RSI})}{TCA_t(X,n_{RSI})} + 1\right) & TCA_t(X,n_{RSI}) \neq 0 \\ 50 & TCA_t(X,n_{RSI}) = 0 \end{matrix}\right .}\)

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.



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.