# Technical Studies Reference

### 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.

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

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.