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### 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.

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.

**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

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*Last modified Friday, 08th March, 2019.