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# Standard Deviation Bands

This study calculates and displays Moving Averages and Standard Deviation Bands of the data specified by the **Top Band Input Data** and **Bottom Band Input Data** Inputs.

Let \(X^{(High)}\) and \(X^{(Low)}\) be random variables denoting the **Top Band Input Data** and **Bottom Band Input Data**, respectively, and let \(X^{(High)}_t\) and \(X^{(Low)}_t\) be their respective values at Index \(t\). Let the Inputs **Length** and **Multplication Factor** be denoted as \(n\) and \(v\), respectively. Then we denote the Top Band and the Bottom Band at Index \(t\) for the given Inputs as \(TB^{(\sigma)}_t\left(X^{(High)},n,v\right)\) and \(BB^{(\sigma)}_t\left(X^{(Low)},n,v\right)\), respectively, and we compute them in terms of Simple Moving Averages and Standard Deviations for \(t \geq n - 1\) as follows.

\(BB^{(\sigma)}_t\left(X^{(Low)},n,v\right) = SMA_t\left(X^{(Low)},n\right) - v\cdot\sigma_t\left(X^{(Low)},n\right)\)

The Simple Moving Averages \(SMA_t\left(X^{(High)},n\right)\) and \(SMA_t\left(X^{(Low)},n\right)\) are also computed and displayed for \(t \geq n - 1\).

**Note**: Depending on the setting of the Input **Moving Average Type**, the Simple Moving Averages in the above calculations could be replaced with Exponential Moving Averages, Linear Regression Moving Averages, Weighted Moving Averages, Wilders Moving Averages, Simple Moving Averages - Skip Zeros, or Smoothed Moving Averages. The types of all Moving Averages in the above calculations are determined by this one Input.

#### 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**.

*Last modified Monday, 03rd October, 2022.