# 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.