# Technical Studies Reference

- Technical Studies Reference
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### KD - Slow

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

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 **Fast %K Length**, **Fast %D Length (Slow %K)**, and **Slow %D Length** be denoted as \(n_{FastK}\), \(n_{FastD}\), and \(n_{SlowD}\), respectively. Then we denote the two indicators for **KD - Slow** at Index \(t\) for the given Inputs as \(Fast\% D_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD})\) and \(Slow\% D_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD},n_{SlowD})\), respectively, and we compute them in terms of Simple Moving Averages for \(t \geq n_{FastK} + n_{FastD} + n_{SlowD}\) as follows.

In the above formula, \(Fast\% K(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK})\) is a random variable denoting the Fast %K for the aforementioned Inputs.

**Note**: For the purposes of computing the Simple Moving Average in the above formula, internal calculations for Fast %K are carried out starting at \(t = n_{FastK} + 2\).

In the above formula, \(Fast\% D(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD})\) is a random variable denoting the Fast %D for the aforementioned Inputs.

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

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

In addition to the graphs of Fast %D and Slow %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 Wednesday, 03rd January, 2018.