QuanTAlib/lib/momentum/aroon/Aroon.md

Aroon

Price levels are irrelevant. The only thing that matters is when they happened. Aroon is a stopwatch for trends.

The Aroon indicator measures the temporal freshness of price extremes. Unlike oscillators that obsess over how much price has moved, Aroon asks how long it has been since a new high or low. It quantifies the "staleness" of a trend, providing an early warning system for consolidation and reversals.

The 1995 Innovation

Tushar Chande introduced Aroon in Beyond Technical Analysis (1995). The name comes from the Sanskrit word for "Dawn's Early Light." Chande's insight was that trends don't just stop; they age. By measuring the time elapsed since the last extreme, Aroon attempts to spot the "dawn" of a new trend rather than just confirming an existing one.

Architecture & Physics

Aroon is purely time-based. It normalizes the "days since" metric into a 0-100 oscillator.

1. Time Tracking: A sliding window of the last N bars is maintained.
2. Extremum Search: The index of the highest high and lowest low within that window is located.
3. Normalization: The distance (in bars) is converted into a percentage.

The Logic of Freshness

• Aroon Up: Quantifies the recency of the High.
  • 100: New high today.
  • 0: No new high for the entire period.
• Aroon Down: Quantifies the recency of the Low.
  • 100: New low today.
  • 0: No new low for the entire period.
• Oscillator: The net difference (Up - Down), showing the dominant temporal force.

Mathematical Foundation

The math is a linear decay function based on time.

\text{Aroon Up} = \frac{Period - \text{Days Since High}}{Period} \times 100

\text{Aroon Down} = \frac{Period - \text{Days Since Low}}{Period} \times 100

\text{Oscillator} = \text{Aroon Up} - \text{Aroon Down}

Performance Profile

While memory is O(P), computational complexity is linear with respect to the period due to the min/max search.

Metric	Complexity	Notes
Throughput	~10ns / bar	Scales linearly with Period (O(P))
Allocations	0 bytes	Hot path is allocation-free
Complexity	O(P)	Requires scanning the buffer for extremes
Memory	O(P)	Stores Period + 1 samples of High and Low

Note: For standard periods (14-50), the linear scan is negligible. For massive periods (>1000), the O(P) cost becomes measurable.

Validation

Validation is performed against standard reference implementations.

• Buffer Sizing: Period + 1 is used to correctly handle the inclusive range.
• Tie-Breaking: If multiple bars share the same extreme value, the most recent one is used (yielding a higher Aroon score).

Common Pitfalls

• Single Value Updates: If you feed Aroon only Close prices (instead of High/Low), it degrades into a "Time Since Highest Close" metric. It works, but it loses the nuance of intraday extremes.
• The 70/30 Rule: A common interpretation is that a trend is strong only if the primary line is > 70. Values between 30 and 70 often indicate noise or consolidation.