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Technical Studies Reference


Moving Average - Hull

This study calculates and displays a Hull Moving Average of the data specified by the Input Data Input. This moving average was developed by Alan Hull.

Let \(X\) be a random variable denoting the Input Data, and let the Input Hull Moving Average Length be denoted as \(n\). Let \(WMA\left(X,\left\lfloor{\frac{n}{2}+\frac{1}{2}}\right\rfloor\right)\) and \(WMA(X,n)\) be random variables denoting the Weighted Moving Averages for \(X\) with Lengths \(\left\lfloor{\frac{n}{2}+\frac{1}{2}}\right\rfloor\) and \(n\), respectively. Then we denote the Moving Average - Hull at Index \(t\) for the given Inputs as \(HMA_t(X,n)\), and we compute it for \(t \geq n + \left\lfloor{\sqrt{n}+\frac{1}{2}}\right\rfloor - 1\) as follows.

\(HMA_t(X,n) = WMA_t\left(2WMA\left(X, \left\lfloor{\frac{n}{2}+\frac{1}{2}}\right\rfloor\right) - WMA(X,n), \left\lfloor{\sqrt{n}+\frac{1}{2}}\right\rfloor\right)\)

For an explanation of the floor function (\(\left\lfloor{\space\space}\right\rfloor\)), refer to our description here.

Inputs

Spreadsheet

The spreadsheet below contains the formulas for this study in Spreadsheet format. Save this Spreadsheet to the Data Files Folder.

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Moving_Average_-_Hull.148.scss


*Last modified Wednesday, 03rd January, 2018.