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### Bill Williams Moving Average

This study calculates and displays a Bill Williams Moving Average of the data specified by the **Input Data** Input.

Let \(X\) be a random variable denoting the **Input Data**, and let \(X_t\) be the value of the **Input Data** at Index \(t\). Let the Input **Length** be denoted as \(n\). Then we denote the **Bill Williams Moving Average** at Index \(t\) for the given Inputs as \(BWMA_t(X,n)\), and we compute it for \(t \geq 0\) as follows.

For \(t = 0\): \(BWMA_0(X,n) = X_0\)

For \(t > 0\): \(\displaystyle{BWMA_t(X,n) = \left(1 - \frac{1}{n}\right)BWMA_{t - 1}(X,n) + \frac{1}{n}X_t}\)

**Note**: Depending on the setting of the Input **Moving Average Type**, the Bill Williams Moving Average in the above calculation could be replaced with a Smoothed Moving Average.

#### Inputs

- Input Data
- MovAvg Length
**Moving Average Type**: This is a custom Input that can be set to either Bill Williams EMA (documented above) or Smoothed Moving Average.

#### 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 Wednesday, 18th April, 2018.