# Kaufman Efficiency Ratio

This study calculates and displays a Kaufman Efficiency Ratio of the data specified by the Input Data Input.

Let $$X$$ be a random variable denoting the Input Data, and let $$X_t$$ be the value of the Input Data at Index $$t$$. Let the Input Length be denoted as $$n$$.

We compute the Direction as follows.

$$|X_t - X_{t - n}|$$

We compute the Volatility as follows.

$$\displaystyle{\sum_{i = t - n + 1}^t |X_i - X_{i - 1}|}$$

The Kaufman Efficiency Ratio at Index $$t$$ is denoted as $$KER_t(X,n)$$. We compute it as follows (provided that the Volatility is not zero).

$$\displaystyle{KER_t(X,n) = \frac{|X_t - X_{t - n}|}{\sum_{i = t - n + 1}^t |X_i - X_{i - 1}|}}$$