Miha Kralj
90d5638008
- 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.
4.4 KiB
AROON: Aroon Indicator
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 amortizedO(1)) - Space:
O(N)— ring buffers for High and Low - Warmup:
Nbars to fill the window
Mathematical Foundation
Parameters
| Symbol | Parameter | Default | Constraint |
|---|---|---|---|
N |
period | 25 | N \geq 1 |
Pseudo-code
Initialize:
highBuf = RingBuffer(period + 1)
lowBuf = RingBuffer(period + 1)
bar_count = 0
On each bar (high, low, isNew):
if !isNew: restore previous state
highBuf.Add(high)
lowBuf.Add(low)
bar_count++
// Find index of highest high in buffer
maxIdx = 0
maxVal = -∞
for i = 0 to min(bar_count, period):
if highBuf[i] >= maxVal:
maxVal = highBuf[i]
maxIdx = i
// Find index of lowest low in buffer
minIdx = 0
minVal = +∞
for i = 0 to min(bar_count, period):
if lowBuf[i] <= minVal:
minVal = lowBuf[i]
minIdx = i
len = min(bar_count, period)
barsSinceHigh = len - maxIdx
barsSinceLow = len - minIdx
AroonUp = (len - barsSinceHigh) / len × 100
AroonDown = (len - barsSinceLow) / len × 100
AroonOsc = AroonUp - AroonDown
output:
Up = AroonUp
Down = AroonDown
Oscillator = AroonOsc
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.
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.pinein indicator directory