# Technical Studies Reference

### Aroon Indicator

This study calculates and displays the Aroon Indicators for the data specified by the Input Data High and Input Data Low Inputs.

Let $$X^{(High)}$$ and $$X^{(Low)}$$ be random variables denoting Input Data High and Input Data Low, respectively, and let $$X^{(High)_t}$$ and $$X^{(Low)}_t$$ be their respective values at Index $$t$$. Let the Input Length be denoted as $$n$$.

Consider the moving window of Length $$n + 1$$ terminating at Index $$t$$ (that is, Indices $$t - n, t - n + 1,...,t$$). We denote the values of the Index of the most recent high of $$X^{(High)}$$ and the most recent low of $$X^{(Low)}$$ in this window as $$T_t^{(Up)}\left(X^{(High)},n\right)$$ and $$T_t^{(Down)}\left(X^{(Low)},n\right)$$, respectively. We compute these, respectively, in terms of a Moving Maximum and a Moving Minimumas follows.

$$T_t^{(Up)}\left(X^{(High)},n\right) = \max\left\{i:X_i^{(High)} > \max_t\left(X^{(High)},n)\right)\right\}$$
$$T_t^{(Down)}\left(X^{(Low)},n\right) = \max\left\{i:X_i^{(Low)} < \min_t\left(X^{(Low)},n)\right)\right\}$$

In the moving window, $$t - T_t^{(Up)}\left(X^{(High)},n\right)$$ is the number of bars since the highest value of $$X^{(High)}$$, and $$t - T_t^{(Down)}\left(X^{(Low)},n\right)$$ is the number of bars since the lowest value of $$X^{(Low)}_t$$.

Finally, we denote the Aroon Indicator Up and Aroon Indicator Down at Index $$t$$ for the given Inputs as $$AI^{(Up)}_t\left(X^{(High)},n\right)$$ and $$AI^{(Down)}_t\left(X^{(Low)},n\right)$$, respectively, and we compute them for $$t \geq 0$$ as follows.

$$\displaystyle{AI^{(Up)}_t\left(X^{(High)},n\right) = 100\cdot\frac{n - \left(t - T_t^{(Up)}\left(X^{(High)},n\right)\right)}{n}}$$

$$\displaystyle{AI^{(Down)}_t\left(X^{(Low)},n\right) = 100\cdot\frac{n - \left(t - T_t^{(Down)}\left(X^{(Low)},n\right)\right)}{n}}$$