# Fisher Relative Vigor Index 3

This study calculates and displays a Fisher Relative Vigor Index (RVI) and Trigger Line for the data given by 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 8.15 and 8.16 of the book Cybernetic Analysis for Stocks and Futures by John Ehlers.

We begin by computing the Stochastic Relative Vigor Index 3, $$RVI^{(Stoch)}_t(n)$$.

Next we denote the Fisher Relative Vigor Index 3 at Index $$t$$ as $$RVI^{(Fish)}_t(n)$$.

If the Use Absolute Value When Log Argument Is Zero Input is set to Yes, then we compute $$RVI^{(Fish)}_t(n)$$ as follows.

$$\displaystyle{RVI^{(Fish)}_t(n) = \frac{1}{2}\ln\left|\frac{1 + 1.98(RVI^{(Stoch)}_t(n) - 0.5)}{1 - 1.98(RVI^{(Stoch)}_t(n) - 0.5)}\right|}$$

This formula is used under the conditions $$\frac{1 + 1.98(RVI^{(Stoch)}_t(n) - 0.5)}{1 - 1.98(RVI^{(Stoch)}_t(n) - 0.5)} \neq 0$$ and $$1 - 1.98(RVI^{(Stoch)}_t(n) - 0.5) \neq 0$$. Otherwise, $$RVI^{(Fish)}_t(n) = 0$$.

If the Use Absolute Value When Log Argument Is Zero Input is set to No, then we compute $$RVI^{(Fish)}_t(n)$$ as follows.

$$\displaystyle{RVI^{(Fish)}_t(n) = \frac{1}{2}\ln\left(\frac{1 + 1.98(RVI^{(Fish)}_t(n) - 0.5)}{1 - 1.98(RVI^{(Fish)}_t(n) - 0.5)}\right)}$$

This formula is used under the conditions $$\frac{1 + 1.98(RVI^{(Fish)}_t(n) - 0.5)}{1 - 1.98(RVI^{(Fish)}_t(n) - 0.5)} > 0$$ and $$1 - 1.98(RVI^{(Fish)}_t(n) - 0.5) \neq 0$$. Otherwise, $$RVI^{(Fish)}_t(n) = 0$$.

Note: For an explanation of the Logarithmic Function ($$\ln()$$), see the documentation here.

The Trigger Line is denoted as $$Trig_t^{(FRVI)}(X,n)$$, and is computed as follows.

$$Trig_t^{(FRVI)}(X,n) = RVI^{(Fish)}_{t - 1}(n)$$

#### Inputs

• Length
• Use Absolute Value When Log Argument Is Zero: This custom Input determines the method of calculation of the Fisher Center of Gravity Oscillator, as described above.