# Technical Studies Reference

This study calculates and displays the Welles Wilder's Average Directional Index Rating (ADXR).

The ADXR is based on calculations similar to those used in the ADX. Just as in that study, the DX Length and DX Mov Avg Length Inputs are denoted as $$n_{DX}$$ and $$n_{\overline{DX}}$$, respectively. $$ADX_t(n_{DX},n_{\overline{DX}})$$ is calculated slightly differently here, as shown below.

$$\displaystyle{ADX_t(n_{DX},n_{\overline{DX}}) = \left\{\begin{matrix} \frac{1}{n_{\overline{DX}}}\sum_{i = 0}^{n_{\overline{DX}} - 1}DX_{t - i}(n_{DX}) & t = n_{DX} + n_{\overline{DX}} - 1 \\ WWMA_t(DX(n_{DX},n_{\overline{DX}}) & t > n_{DX} + n_{\overline{DX}} - 1 \end{matrix}\right .}$$

Let the ADXR Interval Input be denoted as $$n_{ADXR}$$. We denote the ADXR at Index $$t$$ as $$ADXR_t(n_{DX},n_{\overline{DX}},n_{ADXR})$$, and we compute it for $$t \geq n_{DX} + n_{\overline{DX}} + n_{ADXR} - 2$$ as follows.

$$ADXR_t(n_{DX},n_{\overline{DX}},n_{ADXR}) = \frac{1}{2}\left(ADX_t(n_{DX},n_{\overline{DX}}) + ADX_{t - n_{ADXR} + 1}(n_{DX},n_{\overline{DX}}) \right)$$