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# Stochastic

## Double Stochastic

This study calculates and displays the Double Stochastic study.

## Double Stochastic - Bressert

This study calculates and displays the Double Stochastic using the Bressert calculation method.

## KD - Fast

The Stochastic study compares where a symbols price closed relative to its price range over a given time period as specified by the Length Inputs.

## KD - Slow

The Stochastic study compares where a symbols price closed relative to its price range over a given time period as specified by the Length Inputs.

The Stochastic-Slow study differs from Stochastic-Fast, by calculating a moving average of the Fast %D line. This result is known as the Slow %D. The study displays the Fast %D (Slow %K) line and the Slow %D line.

## Preferred Stochastic - DiNapoli

This study calculates a special Stochastic.

## Stochastic - Fast

The Stochastic oscillator compares where a symbol's price closed relative to its price range over a given time period.

## Stochastic - Percentile

The study calculates at each chart bar the percentile rank of the most recent price as specified by the Input Data Input, in a group of prices going back from the current bar by the number of bars specified by the Length Input $$n$$.

The prices are arranged in ascending order and ranked from lowest to highest, starting with a rank of 0. The maximum rank will have a value of Length - 1.

The rank $$R$$ of the most recent price is used to calculate the Stochastic - Percentile $$S$$ as follows.

$$S = \frac{100R}{n - 1}$$

## Stochastic - Slow

The Stochastic oscillator compares where a symbol's price closed relative to its price range over a given time period. The Stochastic-Slow study differs from Stochastic-Fast, by calculating a moving average of the Fast %D line. This result is known as the Slow %D. The study displays the Fast %D (Slow %K) line and the Slow %D line.

## Stochastic Crossover System

The Stochastic Crossover System is a study which displays Up and Down Arrows representing Buy and Sell signals, on the chart based upon the crossover of the Stochastic Slow %K and Slow %D lines.

If Slow %K crosses Slow %D from the bottom and (Slow %K is below Line 2 or Use Buy/Sell Lines is set to No), then a Buy signal is given with an Up Arrow below the Low of the current bar.

If Slow %K crosses Slow %D from the top and (Slow %K is above Line 1 or Use Buy/Sell Lines is set to No), then a Sell signal is given with a Down Arrow above the High of the current bar.

## Stochastic Momentum Indicator

The Stochastic Momentum Indicator study calculates and displays the Stochastic Momentum Indicator.

## Stochastic RSI

Calculates and displays the Stochastic RSI study for Close (Last) Price data. The RSI is used in the calculation.

Let $$C$$ be a random variable denoting the Close Price, and let $$C_t$$ be the value of the Close Price at chart bar $$t$$. Then the RSI of $$C$$ with RSI Length $$n$$ at chart bar $$t$$ is denoted as $$RSI_t(C,n)$$. The type of Moving Average used in the RSI calculation is determined by the RSI Average Type Input.

Let the RSI HighestLowest Length Input be denoted as $$n_{HL}$$. We denote the maximum and minimum values of $$RSI_t(C,n)$$ over a sliding window of Length $$n_{HL}$$ at chart bar $$t$$ as $$MaxRSI_t\left(C,n,n_{HL}\right)$$ and $$MinRSI_t\left(C,n,n_{HL}\right)$$, respectively. We compute them as follows.

$$MaxRSI_t\left(C,n,n_{HL}\right) = \max\{RSI_{t - n_{HL} + 1}(C,n), RSI_{t - n_{HL} + 2}(C,n), ... , RSI_t(C,n)\}$$

$$MinRSI_t\left(C,n,n_{HL}\right) = \min\{RSI_{t - n_{HL} + 1}(C,n), RSI_{t - n_{HL} + 2}(C,n), ... , RSI_t(C,n)\}$$

We denote the Stochastic RSI for the given Inputs at chart bar $$t$$ as $$StochRSI_t\left(C,n,n_{HL}\right)$$, and we compute it with the following recursion relation.

$$StochRSI_0\left(C,n,n_{HL}\right) = 0$$

$$\displaystyle{StochRSI_t\left(C,n,n_{HL}\right) = \left\{ \begin{matrix} \frac{RSI_t(C,n) - MinRSI_t\left(C,n,n_{HL}\right)}{MaxRSI_t\left(C,n,n_{HL}\right) - MinRSI_t\left(C,n,n_{HL}\right)} & MaxRSI_t\left(C,n,n_{HL}\right) - MinRSI_t\left(C,n,n_{HL}\right) \neq 0 \\ StochRSI_{t - 1}\left(C,n,n_{HL}\right) & MaxRSI_t\left(C,n,n_{HL}\right) - MinRSI_t\left(C,n,n_{HL}\right) = 0 \end{matrix}\right .}$$