# Technical Studies Reference

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# 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.

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**.

#### 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.