# Technical Studies Reference

### Fisher Center of Gravity Oscillator

This study calculates and displays a Fisher 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 8.13 and 8.14 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 Center of Gravity Oscillator, $$CG^{(Stoch)}_t(X,n)$$.

Next we denote the Fisher Center of Gravity Oscillator at Index $$t$$ as $$CG^{(Fish)}_t(X,n)$$.

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

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

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

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

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

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

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

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

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

#### Inputs

• Input Data
• 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.