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# Stochastic Function

This study calculates and displays a Stochastic Function and Trigger Line for the data given by the **Input Data** Input. This study is an ACSIL implementation of the Stochastic functions described Chapter 8 of the book *Cybernetic Analysis for Stocks and Futures* by John Ehlers.

Let \(X\) be a random variable denoting the **Input Data**, and let the **Length** Input be denoted as \(n\).

**Note**: This study is not meant to be applied to Price Data. It is meant to be applied to an oscillator.

To apply the Stochastic Function, take the following steps.

- Add the desired oscillator study to a chart.
- Add the Stochastic Function study to a chart.
- Select the Stochastic Function study in the
**Studies to Graph**section of the**Chart Studies**window and click**Settings**. - In the
**Study Settings**window for the Stochastic Function, go to**Based On**and select the oscillator. - For the
**Input Value**of the**Input Data**, select the Subgraph corresponding to the oscillator. - In the
**Study Settings**window, click OK. - In the
**Chart Studies**window, click OK.

We begin by computing the Stochastic Ratio of the Input Data, \(StochRat_t(X,n)\).

Then we compute a smoothed Stochastic Ratio, denoted as \(StochRat_t^{(S)}(X,n)\), which we compute as follows.

\(\displaystyle{StochRat_t^{(S)}(X,n) = \frac{1}{10}\sum_{j = 1}^4 j \cdot StochRat_{t - 4 + j}(X,n)}\)We then compute the **Stochastic Function** for the oscillator, denoted as \(X^{(Stoch)}_t(n)\), as follows.

The Trigger Line for this Indicator is given below.

\(Trig^{(SX)}_t(X,n) = 0.96\left(X^{(Stoch)}_{t - 1}(n) + 0.02\right)\)#### Inputs

*Last modified Monday, 03rd October, 2022.