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# Double Stochastic - Bressert

This study calculates and displays a Bressert's Double Stochastic for the Price Data.

Let \(H\), \(L\), and \(C\) be random variables denoting the High, Low, and Close Prices, respectively, and let \(H_t\), \(L_t\), and \(C_t\) be their respective values at Index \(t\). Let \(n_{HL}\), \(n_{MA}\), and \(n_S\) be the **High & Low Period Length**, **Stochastic Exponential Moving Average Length**, and **Smoothing Length** Inputs, respectively. We then execute the first of two Fast %K and Fast %D calculations, which we denote as \(Fast\%K_t^{(1)}(n)\) and \(Fast\%D_t^{(1)}(n,n_{MA})\), respectively. It should be noted that our calculation of Fast% K is slightly different here than it is in the study KD - Fast. See that study for an explanation of the notation used in the following formulas.

\(Fast\%D_t^{(1)}(n_{HL},n_{MA}) = EMA_t\left(Fast\%K_t^{(1)}(n_{HL}), n_{MA}\right)\)

**Note**: \(Fast\%D_t^{(1)}(n_{HL},n_{MA})\) is referred to as Double Stochastic (DS) Trigger.

Next we execute the second of two Fast %K and Fast %D calculations, which we denote as \(Fast\%K_t^{(2)}(n_{HL},n_{MA})\) and \(Fast\%D_t^{(2)}(n_{HL},n_{MA})\), respectively.

\(Fast\%K_t^{(2)}(n_{HL},n_{MA}) = Fast\%K_t\left(Fast\%D^{(1)}(n_{HL},n_{MA}), Fast\%D^{(1)}(n_{HL},n_{MA}), Fast\%D^{(1)}(n_{HL},n_{MA}), n_{HL}\right)\)\(Fast\%D_t^{(2)}(n_{HL},n_{MA}) = EMA_t\left(Fast\%K^{(2)}(n_{HL},n_{MA}), n_{MA}\right)\)

**Note**: Both of the Fast %D calculations are done using Exponential Moving Averages instead of Simple Moving Averages. There is no Input to change this.

The value of the **Double Stochastic - Bressert** at Index \(t\) is denoted as \(DS^{(B)}_t(n_{HL},n_{MA},n_S)\), and is found by computing an Exponential Moving Average of this second Fast %D calculation.

The Subgraph of both the **Double Stochastic - Bressert** and the DS Trigger are calculated and displayed for \(t \geq 0\).

This study also displays horizontal lines at levels determined by the **Upper Line Value** and **Lower Line Value** Inputs.

#### 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, 26th September, 2022.