# Technical Studies Reference

### 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.

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

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 $$t = n_{FastK} + 2$$.

$$Slow\% D_t(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD},n_{SlowD}) = MA_t(Fast\% D(X^{(High)},X^{(Low)},X^{(Close)},n_{FastK},n_{FastD}),n_{SlowD})$$

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.