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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.

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.