Constructing the average directional index from range expansion and true range

A score of one-sided movement

The average directional index rates trend intensity on a bounded scale from zero to one hundred so different markets can be compared on the same footing. After that rating, high scores are paired with trend-following methods and low scores with range methods.

The average directional index is a twice-smoothed, zero-to-one-hundred score of how intensely recent price movement has been one-sided rather than two-sided. The historical workflow builds that score from range expansion and true range.

One directional increment per session

Each session yields a single directional-movement value: the larger of the high-to-high increment or the low-to-low increment. Both increments are stored as positive numbers.

Plus directional movement is the upward range increment from comparing the current high with the prior high. It is kept only when it is larger than the downward increment. Minus directional movement is the downward range increment from comparing the current low with the prior low. It is labeled minus but stored as a positive quantity.

An outside session keeps the larger excursion beyond the prior range. An inside session is a bar whose high-low range lies inside or matches the prior bar and therefore contributes zero directional movement.

True range as the scale

The directional indicator is that bar’s directional movement expressed as a fraction of the same bar’s true range. True range is the largest of the current high-low span, the current high versus the prior close, and the current low versus the prior close.

Window sums and the smoothed moving sum

The original construction sums plus directional movement, minus directional movement, and true range over fourteen periods, then forms each directional indicator as the matching sum over the true-range sum. Another lookback may replace fourteen.

After the first window, each fourteen-period total is updated by multiplying the prior total by thirteen-fourteenths and adding the new raw observation. That update is a smoothed moving sum: a recursive lookback total that keeps thirteen-fourteenths of the previous window and adds the newest raw observation.

The directional movement index and its average

The directional movement index is the absolute difference of the two fourteen-period directional totals divided by their sum and placed on the zero-to-one-hundred scale. That step records the absolute imbalance between the two smoothed directional-movement totals, scaled by their sum.

The average directional index is the fourteen-period moving average of that index. Once fourteen average-directional-index readings exist, later readings are formed by multiplying the previous average by thirteen-fourteenths and adding the current directional-movement-index value.

When a plus-minus cross is allowed to speak

Illustrated cases associate a high average-directional-index reading with a strong trend and a low reading with a range that later rises when price begins to trend. A fourteen-period plus-minus directional-indicator cross is then described as a directional rule applied only on high-scoring markets.

Editorial reading: the intensity score is assembled first, and the plus-minus cross is considered only after a high score has already ranked the market as trending.