# Random Walk Indicator

This study calculates and displays the High and Low Random Walk Indicators for the Price Data.

Let $$H_t$$ and $$L_t$$ denote, respectively, the High and Low Prices at Index $$t$$, and let the Length Input be denoted as $$n$$. Then we denote the High and Low Random Walk Indicators for the given Input at Index $$t$$ as $$RWI^{(High)}_t(n)$$ and $$RWI^{(Low)}_t(n)$$, respectively. We calculate these for $$t \geq n - 1$$ in terms of the Average True Range as follows.

For $$t = n - 1$$: $$RWI^{(High)}_{n - 1}(n) = RWI^{(Low)}_{n - 1}(n) = 0$$

For $$t > n - 1$$:

$$\displaystyle{RWI^{(High)}_t(n) = \max\left\{0, \frac{H_t - L_{t - 1}}{ATR_{t - 1}(1)\cdot\sqrt{1}}, \frac{H_t - L_{t - 2}}{ATR_{t - 1}(2)\cdot\sqrt{2}}, ..., \frac{H_t - L_{t - n}}{ATR_{t - 1}(n)\cdot\sqrt{n}}\right\}}$$

$$\displaystyle{RWI^{(Low)}_t(n) = \max\left\{0, \frac{H_{t - 1} - L_t}{ATR_{t - 1}(1)\cdot\sqrt{1}}, \frac{H_{t - 2} - L_t}{ATR_{t - 1}(2)\cdot\sqrt{2}}, ..., \frac{H_{t - n} - L_t}{ATR_{t - 1}(n)\cdot\sqrt{n}}\right\}}$$