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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.

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

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

Inputs

Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

Open it through File >> Open Spreadsheet.

Aroon_Indicator.170.scss


*Last modified Monday, 16th April, 2018.