# Technical Studies Reference

### Vertical Horizontal Filter

The Vertical Horizontal Filter determines whether prices are in a trending phase or a congestion phase. Reference: August 1991 issue of Futures magazine, Adam White.

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

The Vertical Horizontal Filter is denoted as $$VHF_t(X,n)$$, and we compute it for $$t \geq n$$ as follows.

$$\displaystyle{VHF_t(X,n) = \frac{\max_t(X,n) - \min_t(X,n)}{\mathrm{sum}_t(X,n)}}$$

In the above formula, the functions $$\max$$, $$\min$$, and $$\mathrm{sum}$$ are the Moving Maximum, Moving Minimum, and Moving Summation, respectively.