# Technical Studies Reference

### Awesome Oscillator / Bill Williams Awesome Oscillator

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

Let $$\overline{P}_t$$ be a random variable denoting the High-Low Average Price, and let $$\overline{P}_t = (H_t + L_t)/2$$ 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 $$AO_t(n_1,n_2)$$, 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.

$$AO_t(n_1,n_2) = MA_t(\overline{P},n_2) - MA_t(\overline{P},n_1)$$

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.