QuanTAlib/lib/dynamics/aroon/Aroon.md

AROON: Aroon Indicator

Aroon measures how recently the highest high and lowest low occurred — recency as a proxy for trend vitality.

Property	Value
Category	Dynamic
Inputs	OHLCV bar (TBar)
Parameters	period
Outputs	Multiple series (Up, Down)
Output range	Varies (see docs)
Warmup	period bars
PineScript	aroon.pine

• The Aroon indicator measures the temporal freshness of price extremes, answering not "how much did price move?" but "how long ago did it make a new...
• Similar: AroonOsc, ADX | Complementary: Volume for confirmation | Trading note: Aroon Up/Down measures time since highest high or lowest low; 100 = new high/low this period.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

The Aroon indicator measures the temporal freshness of price extremes, answering not "how much did price move?" but "how long ago did it make a new high or low?" Aroon Up tracks the recency of the highest high within the lookback window; Aroon Down tracks the recency of the lowest low. Both are normalized to 0-100 where 100 means the extreme occurred on the current bar and 0 means it occurred at the far edge of the window. A companion Aroon Oscillator (Up minus Down) provides a single zero-centered metric for trend bias. Unlike recursive indicators that accumulate floating-point drift, Aroon is purely windowed — its value depends only on data within the lookback period, making it immune to initialization artifacts.

Historical Context

Tushar Chande introduced Aroon in Beyond Technical Analysis (1995). The name comes from the Sanskrit word for "Dawn's Early Light," reflecting the indicator's purpose: to spot the dawn of a new trend rather than merely confirm an existing one. Chande's insight was that trends do not simply stop; they age. A trend that has not made a new high in 20 of the last 25 bars is statistically moribund, regardless of how strong the original breakout was. The temporal perspective inverts the usual analysis framework: instead of asking whether price is above or below some average, Aroon asks whether the market is still making progress in a given direction. This makes it particularly effective at identifying the transition zone between trending and ranging regimes.

Architecture & Physics

1. Sliding Window

A circular buffer of size N+1 stores the last N+1 bars of High and Low values (the current bar plus N historical bars).

2. Extremum Search

On each bar, the buffer is scanned to find the index of the highest high and the index of the lowest low within the window.

3. Aroon Up

\text{AroonUp} = \frac{N - \text{barsSinceHigh}}{N} \times 100

where barsSinceHigh is the number of bars elapsed since the highest high.

4. Aroon Down

\text{AroonDown} = \frac{N - \text{barsSinceLow}}{N} \times 100

5. Aroon Oscillator

\text{AroonOsc} = \text{AroonUp} - \text{AroonDown}

Range: [-100, +100].

6. Complexity

• Time: O(N) per bar for the min/max linear scan (monotonic deque optimization possible for amortized O(1))
• Space: O(N) — ring buffers for High and Low
• Warmup: N bars to fill the window

Mathematical Foundation

Parameters

Symbol	Parameter	Default	Constraint
N	period	25	N \geq 1

Interpretation

Condition	Signal
AroonUp > 70, AroonDown < 30	Strong uptrend (recent highs, stale lows)
AroonDown > 70, AroonUp < 30	Strong downtrend (recent lows, stale highs)
Both > 70	Volatile; both extremes are fresh
Both < 30	Consolidation; both extremes are stale
AroonOsc > 0	Bullish bias
AroonOsc < 0	Bearish bias

Step-Function Behavior

Aroon produces discrete jumps rather than smooth curves. When a new extreme occurs, the corresponding line snaps to 100. Between new extremes, the line decays linearly by 100/N per bar. This staircase pattern is a natural consequence of the temporal measurement and should not be smoothed away — it carries information about the periodicity of extremes.

Performance Profile

Operation Count (Streaming Mode)

Aroon tracks the bar-ago position of the highest high and lowest low using deques (monotone queues) or linear window scans.

Post-warmup steady state (per bar, deque-based O(1) amortized):

Operation	Count	Cost (cycles)	Subtotal
Deque update (high deque, amortized)	2	1	2
Deque update (low deque, amortized)	2	1	2
Index arithmetic (bars since high/low)	2	1	2
MUL × 2 + DIV × 2 (scale to 0–100)	4	5	20
Total	10	—	~26 cycles

~26 cycles per bar at steady state. With naive linear scan: O(N) per bar = 2N comparisons.

Batch Mode (SIMD Analysis)

Operation	Vectorizable?	Notes
Sliding max index (ArgMax)	Partial	SIMD can scan windows in parallel; ArgMax requires horizontal reduction
Sliding min index (ArgMin)	Partial	Same as ArgMax
Position → percentage scaling	Yes	VMULPD + VDIVPD

Batch mode with SIMD prefix-max/min and horizontal ArgMax achieves ~4× throughput on vector-length chunks for the scan phase.

Quality Metrics

Metric	Score	Notes
Accuracy	10/10	Exact integer arithmetic for positions; no floating-point drift
Timeliness	8/10	N-bar lookback; immediate response when new high/low is set
Smoothness	4/10	Output jumps when extreme prices enter or exit the window
Noise Rejection	5/10	Sensitive to outlier bars that reset the extreme-price position

Resources

• Chande, T.S. — Beyond Technical Analysis (John Wiley & Sons, 1995)
• Chande, T.S. — The New Technical Trader (John Wiley & Sons, 1995)
• PineScript reference: aroon.pine in indicator directory