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# Double Stochastic

This study calculates and displays a 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 \(n\) and \(n_{MA}\) be the **Length** and **Moving Average 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.

\(Fast\%D_t^{(1)}(n,n_{MA}) = Fast\%D_t(H,L,C,n,n_{MA}) = SMA_t\left(Fast\%K(H,L,C,n),n_{MA}\right)\)

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

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

**Note**: Depending on the setting of the Input **Moving Average Type**, the Simple Moving Averages in the above Fast %D formulas 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 value of the **Double Stochastic** at Index \(t\) is denoted as \(DS_t(n,n_{MA})\), and it is equal to the value of this second Fast %D calculation.

The Subgraph of the **Double Stochastic** is calculated and displayed for \(t \geq 0\).

This study also displays horizontal lines at levels determined by the **Line 1** and **Line 2** 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.