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Miha Kralj
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- LTMA (Linear Trend Moving Average): Introduces a predictive moving average using dual cascaded EMAs for trend estimation. - MCNMA (McNicholl EMA): Implements a zero-lag TEMA using a cascaded EMA structure for enhanced responsiveness. - NLMA (Non-Lag Moving Average): Utilizes a damped cosine kernel to achieve reduced lag in moving averages. - NMA (Natural Moving Average): Adapts smoothing based on volatility profiles using a square-root kernel. - NYQMA (Nyquist Moving Average): Applies the Nyquist-Shannon theorem to prevent aliasing in cascaded moving averages. - RAIN (Rainbow Moving Average): Combines multiple SMA layers with weighted averages for multi-scale smoothing. - TRAMA (Trend Regularity Adaptive Moving Average): Adapts smoothing based on the frequency of new highs and lows in price data.
114 lines
4.4 KiB
Markdown
114 lines
4.4 KiB
Markdown
# AROON: Aroon Indicator
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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.
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## Historical Context
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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.
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## Architecture & Physics
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### 1. Sliding Window
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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).
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### 2. Extremum Search
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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.
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### 3. Aroon Up
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$$\text{AroonUp} = \frac{N - \text{barsSinceHigh}}{N} \times 100$$
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where barsSinceHigh is the number of bars elapsed since the highest high.
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### 4. Aroon Down
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$$\text{AroonDown} = \frac{N - \text{barsSinceLow}}{N} \times 100$$
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### 5. Aroon Oscillator
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$$\text{AroonOsc} = \text{AroonUp} - \text{AroonDown}$$
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Range: $[-100, +100]$.
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### 6. Complexity
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- **Time:** $O(N)$ per bar for the min/max linear scan (monotonic deque optimization possible for amortized $O(1)$)
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- **Space:** $O(N)$ — ring buffers for High and Low
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- **Warmup:** $N$ bars to fill the window
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## Mathematical Foundation
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### Parameters
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| Symbol | Parameter | Default | Constraint |
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|--------|-----------|---------|------------|
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| $N$ | period | 25 | $N \geq 1$ |
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### Pseudo-code
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```
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Initialize:
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highBuf = RingBuffer(period + 1)
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lowBuf = RingBuffer(period + 1)
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bar_count = 0
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On each bar (high, low, isNew):
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if !isNew: restore previous state
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highBuf.Add(high)
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lowBuf.Add(low)
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bar_count++
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// Find index of highest high in buffer
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maxIdx = 0
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maxVal = -∞
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for i = 0 to min(bar_count, period):
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if highBuf[i] >= maxVal:
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maxVal = highBuf[i]
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maxIdx = i
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// Find index of lowest low in buffer
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minIdx = 0
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minVal = +∞
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for i = 0 to min(bar_count, period):
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if lowBuf[i] <= minVal:
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minVal = lowBuf[i]
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minIdx = i
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len = min(bar_count, period)
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barsSinceHigh = len - maxIdx
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barsSinceLow = len - minIdx
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AroonUp = (len - barsSinceHigh) / len × 100
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AroonDown = (len - barsSinceLow) / len × 100
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AroonOsc = AroonUp - AroonDown
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output:
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Up = AroonUp
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Down = AroonDown
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Oscillator = AroonOsc
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```
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### Interpretation
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| Condition | Signal |
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|-----------|--------|
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| AroonUp > 70, AroonDown < 30 | Strong uptrend (recent highs, stale lows) |
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| AroonDown > 70, AroonUp < 30 | Strong downtrend (recent lows, stale highs) |
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| Both > 70 | Volatile; both extremes are fresh |
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| Both < 30 | Consolidation; both extremes are stale |
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| AroonOsc > 0 | Bullish bias |
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| AroonOsc < 0 | Bearish bias |
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### Step-Function Behavior
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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.
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## Resources
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- Chande, T.S. — *Beyond Technical Analysis* (John Wiley & Sons, 1995)
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- Chande, T.S. — *The New Technical Trader* (John Wiley & Sons, 1995)
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- PineScript reference: `aroon.pine` in indicator directory
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