# Technical Studies Reference

### True Range

This study calculates and displays the True Range of the price data at each Index.

Let the High, Low, and Closing Prices at Index $$t$$ be denoted as $$H_t$$, $$L_t$$, and $$C_t$$, respectively. We then define the following quantities.

High - Low Range: $$H_t - L_t$$

High to Previous Close Difference: $$\left|H_t - C_{t - 1}\right|$$. This is taken to be $$0$$ at $$t = 0$$.

Low to Previous Close Difference: $$\left|L_t - C_{t - 1}\right|$$. This is taken to be $$0$$ at $$t = 0$$.

The True Range at Index $$t$$ is denoted as $$TR_t$$, and we calculate it for $$t \geq 0$$ by taking the maximum of the above quantities, as shown below.

$$TR_t = \max\{H_t - L_t, \left|H_t - C_{t - 1}\right|, \left|L_t - C_{t - 1}\right|\}$$

#### Inputs

This study has no Inputs.