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Description

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.