Function aroon

Aroon (Tushar Chande, 1995) — how recently the window's extremes happened, rather than how far away they are:

aroonUp   = 100 · (period − barsSinceHighestHigh) / period    ${prefix}Up
aroonDown = 100 · (period − barsSinceLowestLow)  / period    ${prefix}Down
aroonOsc  = aroonUp − aroonDown                              ${prefix}Osc
Copy

100 means the extreme is today's bar, 0 means it is the oldest bar still in the window — so a strong uptrend keeps aroonUp pinned near 100 (fresh highs) while aroonDown decays toward 0, and the crossovers are the signal. The name is Sanskrit for "dawn's early light"; Chande's point is that this reads a trend change earlier than an average can, because age moves the instant a new extreme prints while a mean has to be dragged.

Reads high and low (no close), each named by an option defaulting to its DEFAULT_OHLCV column.

The window is period + 1 bars

period counts the oldest age the study can report, and "period bars ago" is itself a reading, so the window has to hold period + 1 bars — the one place in this package where a period is not its window's bar count. The warm-up is therefore period rows, which is what TA-Lib's AROON publishes too (its look-back is exactly period). The rule lives in barsSinceExtremeValues so a second consumer cannot get it wrong.

Definition

TA-Lib's AROON and AROONOSC, exactly: the oracle asserts bar-for- bar agreement with identical warm-up masks on both columns and the oscillator, at period 25 and period 5. There is no smoothing and no seed here, so "exactly" means exactly — unlike the Wilder family, this study has nothing to diverge on.

Ties go to the most recent bar

A new high that merely equals the standing high resets aroonUp to 100. That is TA-Lib's rule (measured: on the window 12, 11, 12, 10.5 at period 4 it reports 75, the newer bar's age, not the older's 25), and it is the reading that matches what the study is for — a market printing an equal high is making a fresh one, not living off an old one.

Edges

• aroonUp and aroonDown are bounded 0..100, and aroonOsc −100..100, by construction: the age is an integer in 0 … period. Both are pinned by property tests.
• Both are invariant to any strictly increasing map of price, not merely a positive scale factor — the study reads the position of the extreme, never its size, so any order-preserving transform (scale, shift, x ** 1.5, …) leaves all three columns bit-identical. A decreasing map swaps the two columns instead. That is a stronger invariance than any other study here has, and the property test asserts it as equality rather than a tolerance.
• A gap costs period + 1 bars and then recovers. The kernel's rule is strict — every cell in the window must be finite — because an extreme taken over the cells you do have is still an honest extreme but its age is not: the hole could be hiding the very bar being asked about. Measured: TA-Lib fed a NaN high skips that bar silently — its comparison against NaN is false — and reports every other bar bit-identical to the clean run, so the hole is invisible in its output and an age counted across it is confidently wrong. pond reports the window as unknown instead.
• A leading gap shifts the start, so running over another study's output starts that many bars later rather than emptying the column.
• The default period is not universal. 25 is the value StockCharts and most charting platforms ship; TA-Lib's own default is 14 (measured), so a vendor comparison should check the length first — the same caveat commodityChannelIndex carries. Aroon is a look-back over positions, so a short window saturates at 100/0 far more often.