# Technical Studies Reference

### Stochastic Relative Vigor Index 3

This study calculates and displays a Stochastic Relative Vigor Index (RVI) and Trigger Line for the Price Data. The RVI used in this study is Relative Vigor Index 3. This study is an ACSIL implementation of the Indicator given in Figures 8.8 and 8.9 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 RVI, $$StochRat_t(RVI(n),n)$$.

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

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

We then compute the Stochastic Relative Vigor Index 3, denoted as $$RVI^{(Stoch)}_t(n)$$, as follows.

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

The Trigger Line for this Indicator is given below.

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