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Technical Studies Reference


Polarized Fractal Efficiency

This study calculates and displays a polarized fractal efficiency for the data specified by the Input Data Input, as well as a moving average of the polarized fractal efficiency.

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 Period Input be denoted as \(n\). Then we denote the Polarized Fractal Effiency at Index \(t\) for the given Inuts as \(PFE_t(X,n)\), and we compute it for \(t \geq n\) as follows.

\(\displaystyle{PFE_t(X,n) = \left\{ \begin{matrix} \frac{\sqrt{(X_t - X_{t - n})^2 + n^2}}{\sum_{i = t - n + 2}^t \sqrt{(X_i - X_{i - 1})^2 +1}} & X_t \geq X_{t - 1} \\ -\frac{\sqrt{(X_t - X_{t - n})^2 + n^2}}{\sum_{i = t - n + 2}^t \sqrt{(X_i - X_{i - 1})^2 +1}} & X_t < X_{t - 1} \end{matrix}\right .}\)

Let the Smoothing Period Input be denoted as \(n_S\). We denote the Smoothed Polarized Fractal Efficiency at Index \(t\) for the given Inputs as \(PFE^{(S)}(X,n,n_S)\), and we compute it for \(t \geq n\) in terms of an Exponential Moving Average as follows.

\(PFE^{(S)}(X,n,n_S) = EMA_t(PFE(X,n),n_S)\)

Note: Depending on the setting of the Input Moving Average Type, the Exponential Moving Average in the above calculation could be replaced with a Linear Regression Moving Average, a Simple Moving Average, a Weighted Moving Average, a Wilders Moving Average, a Simple Moving Average - Skip Zeros, or a Smoothed Moving Average.

Inputs

Spreadsheet

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Open it through File >> Open Spreadsheet.

Polarized_Fractal_Efficiency.434.scss


*Last modified Friday, 08th March, 2019.