# Technical Studies Reference

This study calculates and displays a Traders Dynamic Index (TDI) of the data specified by the RSI Price Input. The TDI consists of five Subgraphs. This study relies on the studies RSI and Bollinger Bands. See the documentation of those studies for an explanation of the notation used here.

Let the RSI Price at Index $$t$$ be given by $$X_t$$. Let the RSI Length, Volatility Band Length, RSI Price Line, and RSI Trade Signal Line Inputs be denoted as $$n_{RSI}$$, $$n_{Vol}$$, $$n_{PL}$$, and $$n_{TSL}$$, respectively.

The five Subgraphs of the TDI are computed for $$t \geq 0$$. The first two of them are moving averages of the RSI.

$$\displaystyle{\overline{RSI}_t\left(X,n_{RSI},n_{PL}\right) = SMA_t\left(RSI\left(X,n_{RSI}\right),n_{PL}\right)}$$

Note: The Moving Average Type in the above formula is determined by the RSI Price Type Input.

$$\displaystyle{\overline{RSI}_t\left(X,n_{RSI},n_{TSL}\right) = SMA_t\left(RSI\left(X,n_{RSI}\right),n_{TSL}\right)}$$

Note: The Moving Average Type in the above formula is determined by the Trade Signal Type Input.

The remaining three Subgraphs are the Top, Middle, and Bottom Volatility Bands. The values of these Subgraphs at Index $$t$$ are denoted as $$TB^{(Vol)}_t\left(X, n_{RSI}, n_{Vol}\right)$$, and $$BB^{(Vol)}_t\left(X, n_{RSI}, n_{Vol}\right)$$, $$TB^{(Vol)}_t\left(X, n_{RSI}, n_{Vol}\right)$$, respectively. These Bollinger Bands of the RSI, as we indicate below.

$$TB^{(Vol)}_t\left(X, n_{RSI}, n_{Vol}\right) = TB^{(BB)}_t\left(RSI\left(X,n_{RSI}\right), n_{Vol}, 1.6185\right)$$
$$MB^{(Vol)}_t\left(X, n_{RSI}, n_{Vol}\right) = MB^{(BB)}_t\left(RSI\left(X,n_{RSI}\right), n_{Vol}, 1.6185\right)$$
$$BB^{(Vol)}_t\left(X, n_{RSI}, n_{Vol}\right) = BB^{(BB)}_t\left(RSI\left(X,n_{RSI}\right), n_{Vol}, 1.6185\right)$$