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Technical Studies Reference

Bollinger Bands


This study calculates and displays Bollinger Bands for the data specified by the Input Data Input, as well as a Moving Average of the Input Data.

Let \(X\) be a random variable denoting the Input Data, and let \(X_i\) be the value of the Input Data at Index \(i\). Let the Inputs Length and Standard Deviations be denoted as \(n\) and \(v\), respectively. Then we denote the Bollinger Bands at Index \(t\) for the given Inputs as \(TB^{(B)}_t(X,n,v)\) (Top Band), \(MB^{(B)}_t(X,n,v)\) (Middle Band), and \(BB^{(B)}_t(X,n,v)\) (Bottom Band), and we compute them for \(t \geq n - 1\) in terms of a Simple Moving Average and a Standard Deviation as follows.

Top Band: \(TB^{(B)}_t(X,n,v) = SMA_t(X,n) + v \cdot \sigma_t(X,n)\)

Middle Band: \(MB^{(B)}_t(X,n,v) = SMA_t(X,n)\)

Bottom Band: \(BB^{(B)}_t(X,n,v) = SMA_t(X,n) - v \cdot \sigma_t(X,n)\)

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



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*Last modified Wednesday, 05th July, 2023.