# Technical Studies Reference

### Stochastic Center of Gravity Oscillator

This study calculates and displays a Stochastic Center of Gravity Oscillator and Trigger Line for the data given by the Input Data Input. This study is an ACSIL implementation of the Indicator given in Figures 8.6 and 8.7 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 $$n$$.

We begin by computing the Stochastic Ratio of the Center of Gravity Oscillator, $$StochRat_t(CG(X,n),n)$$.

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

$$\displaystyle{StochRat_t^{(S)}(CG(X,n),n) = \frac{1}{10}\sum_{j = 1}^4 j \cdot StochRat_{t - 4 + j}(CG(X,n),n)}$$

We then compute the Stochastic Center of Gravity Oscillator, denoted as $$CG^{(Stoch)}_t(X,n)$$, as follows.

$$CG^{(Stoch)}_t(X,n) = 2\left(StochRat_t^{(S)}(CG(X,n),n) - 0.5\right)$$

The Trigger Line for this Indicator is given below.

$$Trig^{(SCG)}_t(X,n) = 0.96\left(CG^{(Stoch)}_{t - 1}(X,n) + 0.02\right)$$