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⏱️ Aroon — Time-Since-Extreme Indicator

Aroon measures when, not how much: how many periods have elapsed since the highest high and the lowest low within a lookback window. A fresh new trend shows up as "time since extreme" collapsing toward zero.

💡 Financial Meaning

Aroon Up spikes to 100 the moment price sets a new \(N\)-period high; it decays linearly if no new high appears. The same logic, mirrored, drives Aroon Down from the lowest low. A crossover of Aroon Up above Aroon Down — especially near 100 — signals the birth of an uptrend; the reverse signals a new downtrend. The Aroon Oscillator (Up − Down) condenses both lines into one, oscillating between −100 and +100.

🔢 Mathematical Formulas

  1. Periods since the highest high / lowest low within the last \(N\) observations:

    \[ p^{H}_t = \operatorname*{argmax}_{0 \le i \le N} H_{t-i}, \qquad p^{L}_t = \operatorname*{argmax}_{0 \le i \le N} \big(-L_{t-i}\big) \]

  2. Aroon Up / Down, rescaling elapsed time into a 0–100 "freshness" score:

    \[ Up_t = 100 \cdot \frac{N - p^{H}_t}{N}, \qquad Down_t = 100 \cdot \frac{N - p^{L}_t}{N} \]

  3. Aroon Oscillator:

    \[ Osc_t = Up_t - Down_t \]

⚙️ Parameters

Parameter Key Default Description
Period (\(N\)) period 14 Lookback window for locating the extreme high/low, in sessions.

🎛️ Signal Processing Equivalent — Peak-Hold Timer / Age Counter

Aroon is unusual among these indicators: it is not a filter on amplitude at all, but a peak-hold circuit with an age counter. Each new sample resets a "time-since-last-peak" register to zero if it beats the running maximum within the window; otherwise the register counts up. This is the discrete-time equivalent of a retriggerable monostable timer driven by a comparator against a sliding-window maximum/minimum.

flowchart LR
    H["📈 High"] --> MAXW["🏔️ Rolling max over N bars"]
    MAXW --> AGEH["⏱️ Bars since last new high"]
    AGEH --> UP["⬆️ Aroon Up = 100·(N−age)/N"]
    L["📉 Low"] --> MINW["🕳️ Rolling min over N bars"]
    MINW --> AGEL["⏱️ Bars since last new low"]
    AGEL --> DOWN["⬇️ Aroon Down = 100·(N−age)/N"]
    UP --> OSC["🔄 Oscillator = Up − Down"]
    DOWN --> OSC

Complementary to ADX

ADX measures directional energy accumulated over the window; Aroon measures elapsed time since the last extreme. A trend can be strong by ADX's measure while Aroon shows it is "aging" (no new extreme for a while) — a common early warning of exhaustion that ADX alone will not show.

Aroon indicator on Wikipedia