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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 \(WMA\left(X,\left\lfloor{\frac{n}{2}}\right\rfloor\right)\) and \(WMA(X,n)\) be random variables denoting the Weighted Moving Averages for \(X\) with Lengths \(\left\lfloor{\frac{n}{2}}\right\rfloor\) 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.

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

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.

Open it through File >> Open Spreadsheet.

Moving_Average_-_Hull.148.scss


*Last modified Tuesday, 27th September, 2022.