Average Directional Index construction with frozen true range and directional rules

A model defined once

Average Directional Index is a trend-strength model assembled from true range and the two exclusive directional-movement increments over a chosen sampling interval and lookback. Construction on each bar starts with three quantities: true range, plus directional movement, and minus directional movement.

Editorial reading: those three quantities are frozen bar rules. Once they are written as named seed formulas, the same definition is projected across the ordered sample instead of being rewritten on every observation. The archive records the historical workflow. The frozen-rule reading is editorial and is not attributed to the archive.

True range

True range is the largest of a bar's high-to-low width and the two absolute gaps between that bar's extremes and the prior close. In construction, compare the bar's high-to-low span, the absolute gap from the prior close to the current high, and the absolute gap from the prior close to the current low. Keep the largest of those three measures as that bar's true range.

Exclusive directional increments

Plus directional movement is the upward extension kept only when the current high makes the dominant advance versus the prior bar. The plus directional increment equals the current high minus the prior high on a clear up bar, or on an outside bar whose upside extension exceeds its downside extension. Otherwise that increment is stored as a missing value.

Minus directional movement is the downward extension kept only when the current low makes the dominant decline versus the prior bar. The minus directional increment equals the prior low minus the current low on a clear down bar, or on an outside bar whose downside extension exceeds its upside extension. Otherwise that increment is stored as a missing value.

An outside bar both exceeds the prior high and breaks the prior low, so only the larger extension is retained. Nested conditionals implement that outside-bar tie-break: only the dominant extension is kept, and the opposite directional increment is left without a directional value.

Named ranges and static formula fill

Named ranges identify the price block, the three seed formulas, and the result columns so each Average Directional Index component can be filled from a single unchanging definition.

When the construction formulas do not change from bar to bar, the working method is static formula fill. Copy each named seed formula down its column and convert the copies to values, leaving only the original formula cells live.

Indexed write loops and position counters are reserved for procedures in which the text of each calculated line actually changes while the loop runs. They are not the working method when the construction rules stay the same from bar to bar.

Missing-value markers

A missing-value marker is a non-numeric placeholder that keeps a non-qualifying bar off a chart instead of plotting as zero. Seed rows and non-qualifying directional cells should hold missing-value markers. Blank-text placeholders can plot as zero and shrink the chart scale.

Extending the sample

Lengthening the last row of the named input and result ranges extends the sample while leaving the same true-range and directional-increment rules in force. The seed definitions do not need to be rewritten when the ordered sample grows.