Vertical Horizontal Filter (VHF)

Summary

Vertical Horizontal Filter: Adam White's trend-versus-range filter, the range a window covered divided by the path it actually travelled.

Bounded in [0,1]. Values near 1 mean the market covered most of its path in one direction (trending); values near 0 mean it retraced repeatedly and went nowhere (choppy). Like ADX it measures trend strength, not direction, but it uses no smoothing and carries no recursion.

A common use is regime selection: run trend-following logic while VHF is high, oscillator logic while it is low.

Formula

num = MAX(C[t-optInTimePeriod+1..t]) - MIN(C[t-optInTimePeriod+1..t]), the range spanned by the optInTimePeriod most recent closes. den = SUM( |C[j] - C[j-1]| ) for j = t-optInTimePeriod+1 .. t, the total absolute movement over the same number of changes, which therefore reaches one close further back. VHF = num / den.

The two windows are deliberately not co-terminal: the extrema span optInTimePeriod closes, the changes consume one more. Because num is the distance between two points the changes connect, num <= den always, so the result never leaves [0,1].

Notes

A window whose closes are all identical has no vertical movement and no horizontal movement. VHF reports 0 there. Other libraries differ: Tulip Indicators leaves the division unguarded and emits NaN, pandas-ta-classic perturbs the numerator and emits +Inf.
Adam White later described an 18-bar VHF smoothed by a 6-bar moving average. That variant is not implemented here; apply a moving average to outReal to obtain it.