Technical Studies Reference

Preferred Stochastic - DiNapoli

This study calculates and displays both the Fast %D (aka Slow %K) and Slow %D stochastic indicators for the data specified by the High, Low, and Closing Prices. These indicators are described in the documentation for the KD - Slow, and they are based on the Fast %K indicator, which is described in the documentation for the study KD - Fast.

Let \(H\), \(L\), and \(C\) be random variables denoting the High, Low, and Closing Prices, respectively. Let the Inputs Fast %K Length, Fast %D Average Length (Slow %K), Modified Average Length (Slow %D) be denoted as \(n_{FastK}\), \(n_{FastD}\), and \(n_{SlowD}\), respectively.

We calculate Fast %D for \(t \geq 0\) in terms of an Exponential Moving Average as follows.

\(Fast\% D_t(H,L,C,n_{FastK},n_{FastD}) = EMA_t(Fast\% K(H,L,C,n_{FastK}),n_{FastD})\)

We calculate Slow %D for \(t \geq 0\) in terms of a Modified Moving Average, which is defined as follows.

\(Slow\% D_t(H,L,C,n_{FastK},n_{FastD},n_{SlowD}) = Slow\% D_{t - 1}(H,L,C,n_{FastK},n_{FastD},n_{SlowD}) + (Fast\% D_t(H,L,C,n_{FastK},n_{FastD}) - Slow\% D_{t - 1}(H,L,C,n_{FastK},n_{FastD},n_{SlowD}))/n_{SlowD}\)

Note: For both Fast %D and Slow %D, only the values for \(t \geq n_{FastK} + n_{FastD} + 1\) are displayed as output.

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 Wednesday, 03rd January, 2018.