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# Choppiness Index

This study calculates and displays a Choppiness Index of the price data.

Let \(H\) and \(L\) be random variables denoting the High Price and Low Price, respectively, and let \(H_t\) and \(L_t\) be their respective values at Index \(t\). Let the Inputs **Summation Period** and **ATR Period** be denoted as \(n_S\) and \(n_{ATR}\), respectively. Let \(ATR(n_{ATR})\) denote the Average True Range with Length \(n_{ATR}\). Then we denote the **Choppiness Index** at Index \(t\) for the given Inputs as \(CI_t(n_S,n_{ATR})\), and we compute it as follows.

This Subgraph is displayed for \(t > \max(n_S, n_{ATR}) - 1\).

The above formula is used as long as \(\max_t(H,n_S) - \min_t(L,n_S) \neq 0\). Otherwise, \(CI_t(n_S,n_{ATR}) = 0\).

For an explanation of the Sigma (\(\Sigma\)) notation for summation, refer to our description here: Summation.

For an explanation of the functions \(\max_t()\) and \(\min_t()\), refer to our descriptions here: Moving Maximum and Moving Minimum.

#### 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**.

*Last modified Monday, 26th September, 2022.