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Technical Studies Reference

KD - Fast

This study calculates and displays both the Fast %K and the Fast %D stochastic indicators for the data specified by the Input Data for High, Input Data for Low, and Input Data for Last Inputs.

Let \(X^{(High)}\), \(X^{(Low)}\), and \(X^{(Close)}\) be random variables denoting the Input Data for High, Input Data for Low, and Input Data for Last, respectively, and let \(X_t^{(High)}\), \(X_t^{(Low)}\), and \(X_t^{(Last)}\) be their respective values at Index \(t\). Let the Inputs %K Length and %D Length be denoted as \(n_{FastK}\) and \(n_{FastD}\), respectively. The two indicators for KD - Fast are Fast%K and Fast%D (aka Slow%K). We compute them for \(t \geq n_{FastK} + n_{FastD}\) as follows.

\(Fast\% K_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK}) = \displaystyle{\left\{ \begin{matrix} 100\cdot\frac{X_t^{(Close)} - \min_t\left(X_t^{(Low)},n_{FastK}\right)}{\max\left(X_t^{(High)},n_{FastK}\right) - \min_t\left(X_t^{(Low)},n_{FastK}\right)} & \max\left(X_t^{(High)},n_{FastK}\right) - \min_t\left(X_t^{(Low)},n_{FastK}\right) \neq 0 \\ 100 & \max\left(X_t^{(High)},n_{FastK}\right) - \min_t\left(X_t^{(Low)},n_{FastK}\right) = 0 \end{matrix}\right .}\)

For an explanation of the \(\min\) and \(\max\) functions in the above formula, see our descriptions of the Moving Minimum and Moving Maximum.

Fast %D is calculated in terms of a Simple Moving Average, as shown below.

\(Fast\% D_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD}) = SMA_t(Fast\% K(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK}),n_{FastD})\)

Note: For the purposes of computing the Simple Moving Average in the above formula, internal calculations for Fast %K are carried out for \(n_{FastK} + 1 \leq t < n_{FastK} + n_{FastD}\). These values are not displayed as output.

Note: Depending on the setting of the Input Moving Average Type, the Simple Moving Average in the above formula 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.

In addition to the graphs of Fast %K and Fast %D, this study also displays two horizontal lines whose levels are determined by the Inputs Line1 Value and Line2 Value.



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.