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# Bill Williams Awesome Oscillator

### Description

This study calculates and displays the Bill Williams Awesome Oscillator of the High-Low Average Price.

Let \(\overline{P}^{(HL)}\) be a random variable denoting the High-Low Average Price, and let \(\overline{P}_t^{(HL)} = (H_t + L_t)/2\) be the value of the High-Low Average Price at Index \(t\). Let the Inputs **Moving Average 1 Length** and **Moving Average 2 Length** be denoted as \(n_1\) and \(n_2\), respectively. Then **Bill Williams Awesome Oscillator** at Index \(t\) for the given Inputs as is denoted as \(AO_t\left(\overline{P}^{(HL)},n_1,n_2\right)\), and it is calculated in terms of Simple Moving Averages for \(t \geq \max\{n_1,n_2\} - 1\) (Study 72) and for \(t \geq \max\{n_1,n_2\}\) (Study 162) as follows.

**Note**: Depending on the setting of the Input **Moving Average Type**, the Simple Moving Averages in the calculation of \(AO_t(n_1,n_2)\) could be replaced with Exponential Moving Averages, Linear Regression Moving Averages, Weighted Moving Averages, Wilders Moving Averages, Simple Moving Averages - Skip Zeros, or Smoothed Moving Averages. The types of both Moving Averages in the calculation are determined by this one Input.

#### 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 Tuesday, 31st January, 2023.