# Technical Studies Reference

### AC DC Histogram - Bill Williams Acceleration Deceleration Oscillator

This study calculates and displays the Bill Williams Acceleration/Deceleration Oscillator. It is computed using four Simple Moving Averages with Lengths $$n_1$$, $$n_2$$, $$n_3$$, and $$n_4$$. All four moving averages use the same Input Data.

We begin by finding $$\Delta MA_t(X,n_2,n_1)$$, the difference of the moving averages with lengths $$n_1$$ and $$n_2$$ at Index $$t$$.

$$\Delta MA_t(X,n_2,n_1) = MA_t(X,n_2) - MA_t(X,n_1)$$

The height of the AC/DC Histogram at Index $$t$$ for the given Inputs is denoted as $$ACDC_t(X,n_1,n_2,n_3,n_4)$$. We compute this for $$t \geq \max\{n_1,n_2\} + n_3 + n_4$$ as follows.

$$ACDC_t(X,n_1,n_2,n_3,n_4) = MA_t((\Delta MA(X,n_2,n_1) - MA(\Delta MA(X,n_2,n_1),n_4)),n_3)$$

In the above formula, $$\Delta MA(X,n_2,n_1)$$ is a random variable corresponding to $$\Delta MA_t(X,n_2,n_1)$$.

#### Inputs

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.