True-range-scaled construction of the vortex indicator

What the vortex pair reports

The vortex indicator is a two-line directional construction. It sums crossed bar extremes over a lookback, scales each sum by the same true-range total, and treats interaction of the lines as a directional signal.

Each bar contributes vortex movement in both directions. The upward increment is the absolute gap from the current high to the prior low. The downward increment is the absolute gap from the current low to the prior high.

One lookback and a shared budget

Each vortex line is the lookback sum of its increments divided by the lookback sum of true range, so both lines share one range budget. Lookback-length is the number of bars over which vortex movement and true range are summed before the two ratios are formed.

Implementations apply one integer lookback to both increment sums and the true-range sum, and they commonly default that lookback to 14 bars. The two ratios are formed only when the lookback true-range sum is not zero.

One implementation splits the construction into two independently configurable lookbacks: one for the vortex increment sums and another for the true-range sum.

How true range is taken

True range in the shared denominator is the largest of the current high-low span and the two distances from the prior close to the current high and current low. Vortex plus is that upward lookback sum divided by this true-range total. Vortex minus is the matching downward ratio.

Crossover, signed spread, and companion entries

A change-of-direction hypothesis is defined as a vortex crossover, the event in which the upward line crosses the downward line. Some constructions also collapse the pair into a signed vortex spread, a single series equal to the upward line minus the downward line.

Companion rule sets place a stop entry at the signal bar's high after an upward cross and at the signal bar's low after a downward cross.

Both increment series stay live

Relative to classic directional movement, this construction keeps both increment series live on every bar, including inside bars, instead of assigning zero to the smaller outside-range extension.