Indicator library · Trend
ADXR, The Smoothed Directional Index
Today’s ADX averaged with the ADX of n bars ago. Two values, one division, and a line built for ranking several instruments at once rather than for watching one.
The calculation
ADXR = (ADX today + ADX n periods ago) ÷ 2, with n conventionally 14, the same period used for ADX itself.
Two things about that formula are worth pausing on, because most descriptions of ADXR are one sentence long and skip both. It is not a moving average: only two values enter it, and everything between them is discarded. And it inherits every property of ADX underneath (the three stacked smoothings, the absolute value that throws away direction, the long dependence on where the data started) then adds one more step on top.
What the averaging costs and buys
| Property | ADX | ADXR |
|---|---|---|
| Responsiveness | Late already, three smoothings. | Later again, by roughly half the period. |
| Range of the reading | Reaches its own extremes. | Compressed: it can never exceed the higher of the two values it averages. |
| Stability for ranking | Order changes on ordinary noise. | Steadier, which is the job Wilder built it for. |
| Sensitivity to one bar | Diluted across the smoothing. | Half the reading is a single past value, so an outlier n bars back carries weight. |
That last row is the property people are surprised by. Because ADXR averages two points rather than a window, an unusual reading nine or fourteen bars ago is not diluted. It is half of today’s answer, until it drops out of the comparison entirely and the line steps. A true moving average of ADX would behave more gently and would also be a different indicator.
Where it belongs
Wilder introduced ADXR inside the Commodity Selection Index, a ranking system: several markets, one question (which is currently most worth trading), and a need for an answer that does not reshuffle on noise. That is still where it earns its place.
For watching one instrument, ADX is the better line: it says the same thing sooner, and the extra lag buys nothing you need when the alternative is simply looking at the price beside it. If both are on screen, read them as one reading rather than two. They share every input, so their agreement confirms nothing at all.
The step nobody expects
One behaviour follows directly from averaging exactly two points and surprises people who assume a smoothing. When the value from n bars ago finally drops out of the comparison, the reading can move noticeably on a session where ADX barely changed, half of the answer was just replaced. A true moving average of ADX would have retired that value gradually.
In practice the effect is small on quiet data and visible after an unusual stretch: an instrument that trended hard n bars ago and has been calm since will show ADXR stepping down when that reading leaves, with nothing in the market to explain it. The lesson is the same as for the simple moving average elsewhere in this library, when a line moves on a day when nothing happened, check what left the window before looking for a cause in the price.
Where it misleads
| Situation | What goes wrong |
|---|---|
| Treated as a moving average | Only two values enter it. An outlier n bars back is half the reading rather than one point in a window. |
| ADX thresholds reused | The averaging compresses the range, so 25 is reached less often and means something slightly different. |
| Read as confirmation of ADX | They share every input. Two views of one calculation are not two pieces of evidence. |
| Used as an entry trigger | Later than a measure that was already late. Nothing about this line is timely. |
| Read as directional | It inherits the absolute value in DX, a decline and an advance produce identical readings. |
| Short history | It sits on top of ADX, which sits on Wilder smoothing; early values depend on where the series began. |
Reproducing it
Two implementations of ADXR frequently disagree, and the cause is almost never the final division. It is either the lookback (some platforms fix the ADXR offset at 14 regardless of the ADX period, others tie the two together), or the amount of history fed in, because ADX itself carries its Wilder seed forward for a very long time. Two lines that differ over the first hundred bars and converge afterwards are usually both correct.
The check that isolates it takes a minute: compare the underlying ADX series first. If those agree and the ADXR lines do not, the offset is the difference; if the ADX lines already differ, nothing about ADXR is worth debugging until that is settled. As everywhere in this library, the convention matters more than the arithmetic, and stating which one you used is what makes a published figure checkable.
What volume adds
Like ADX, this line is computed from highs, lows and closes, so it can report a trend as strongly consistent without any knowledge of how many participants were involved. In a ranking context (which is where ADXR belongs), that gap matters more than usual, because the instruments being compared may differ enormously in how much is traded in them.
Ranking on trend strength alone will happily put a thinly traded instrument at the top of the list, where the consistency is a property of an empty book rather than of a market. A dollar volume floor applied before the ranking removes that failure, and costs one column.
Frequently asked questions
How is ADXR calculated?
ADXR = (today’s ADX + the ADX of n periods ago) ÷ 2, with n conventionally the same period used for ADX itself, 14. That is the whole formula. It is not a moving average of ADX, which is what most people assume: only two values enter it, today’s and one from exactly n bars back, and everything between them is ignored.
Why did Wilder include it at all?
As a steadier reading for ranking instruments rather than for reading one chart. Wilder used ADXR in his Commodity Selection Index, where the question was which of several markets was most worth trading, a comparison that a jumpy reading makes unstable, since the ranking changes on noise. Averaging today against a fixed point n bars back damps that without adding another smoothing pass over the whole series.
Is ADXR just a smoothed ADX?
It is smoother, and it is not a smoothing in the usual sense. A moving average of ADX would use every value in its window; ADXR uses exactly two, so it can be affected by what an ordinary average would have diluted, if the reading n bars ago happened to be an outlier, half of today’s ADXR is that outlier. The distinction is small in practice and it explains occasional behaviour that a true average would not produce.
What does it add over reading ADX itself?
Stability at the cost of timeliness, and very little else. On a single chart the two lines tell the same story with ADXR arriving later and moving less; anyone watching one instrument is generally better served by ADX. ADXR earns its place where several instruments are being compared on trend strength at the same moment, which is exactly the job Wilder built it for.
How much later is it?
Roughly half the period, in the sense that averaging a value with one from n bars back pulls the result about halfway toward where the reading was then. On a 14-period setting the effect is a line that turns several bars after ADX does and reaches a lower peak in a fast trend. On the series charted on this page ADX peaks well above ADXR, and the gap is entirely the averaging.
Does it have its own thresholds?
The same conventions are usually applied — 20 and 25 — and they fit slightly less well, because ADXR compresses the range: it cannot exceed the higher of the two values it averages, so extremes are trimmed by construction. If a threshold is going to be acted on, derive it from the same instrument’s own ADXR history rather than borrowing the ADX levels.
Which one should I plot?
ADX for a single instrument, ADXR when ranking several. If you plot both, treat them as one reading rather than two. They share every input, so their agreement is not confirmation of anything. The only genuinely additional information in having both on screen is the gap between them, which is a rough measure of how quickly trend strength has been changing.
Is it available in most software?
Yes, and implementations agree less often than the simple formula suggests. The two common differences are the period used for the lookback, some platforms fix it at 14 regardless of the ADX period, and the amount of history fed in, since ADX itself carries its Wilder seed forward for a long time. Two ADXR lines that differ in the first hundred bars and converge later are usually both correct.