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.
4.1 KiB
AROONOSC: Aroon Oscillator
The Aroon Oscillator condenses the dual-line Aroon system into a single zero-centered value by computing \text{AroonUp} - \text{AroonDown}. This distills the temporal battle between fresh highs and fresh lows into a bounded [-100, +100] metric where positive values indicate bullish recency dominance and negative values indicate bearish. Unlike recursive indicators that accumulate floating-point drift, the Aroon Oscillator is purely windowed — its value depends only on data within the lookback period, making it stateless in the long term and immune to initialization poisoning. The step-function output reflects discrete events (new extremes appearing or aging out) rather than smooth price trajectories.
Historical Context
Tushar Chande introduced the Aroon system in The New Technical Trader (1995) as a departure from price-magnitude momentum. While RSI and MACD ask "how much did price move?", Aroon asks "how long has it been since the last extreme?" The Oscillator is the net verdict of this temporal argument. Chande's key observation was that the recency of extremes carries more information about trend health than the magnitude of movements. A market making new highs every few bars is trending up regardless of the size of each increment. The Oscillator pegs at +100 when a new high appears on every bar within the window (maximum bullish freshness), and at -100 when new lows dominate. The middle ground (values near zero) indicates neither extreme is particularly fresh — the temporal signature of consolidation.
Architecture & Physics
1. Sliding Window Buffers
Two ring buffers of size N+1 store the last N+1 bars of High and Low values.
2. Extremum Location
On each bar, scan the buffers to locate the index of the highest high and the lowest low.
3. Aroon Components
\text{AroonUp} = \frac{N - \text{barsSinceHigh}}{N} \times 100
\text{AroonDown} = \frac{N - \text{barsSinceLow}}{N} \times 100
4. Oscillator
\text{AroonOsc} = \text{AroonUp} - \text{AroonDown}
5. Complexity
- Time:
O(N)per bar for min/max scanning - Space:
O(N)— two ring buffers - 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++
len = min(bar_count, period)
// Scan for extremes
maxIdx = index of maximum in highBuf over last (len + 1) entries
minIdx = index of minimum in lowBuf over last (len + 1) entries
barsSinceHigh = len - maxIdx
barsSinceLow = len - minIdx
AroonUp = (len - barsSinceHigh) / len × 100
AroonDown = (len - barsSinceLow) / len × 100
output = AroonUp - AroonDown
Drift Immunity
Unlike EMA-based oscillators that accumulate rounding errors across thousands of bars, the Aroon Oscillator is computed fresh each bar from a finite window. There is no recursive state that can diverge. This makes it architecturally robust for long-running production systems where indicator drift is a concern.
Interpretation
| AroonOsc Value | Meaning |
|---|---|
| +100 | New high every bar; no new lows (maximum bullish) |
| +50 to +100 | Strong bullish bias; highs are fresh |
| 0 | Balanced; both extremes equally stale/fresh |
| -50 to -100 | Strong bearish bias; lows are fresh |
| -100 | New low every bar; no new highs (maximum bearish) |
Flatlining Behavior
In strong trends, the oscillator can hold +100 or -100 for sustained periods. This indicates a continuously refreshing extreme — the market is making a new high (or low) on virtually every bar. This is not saturation; it is the temporal signature of a parabolic move.
Resources
- Chande, T.S. — The New Technical Trader (John Wiley & Sons, 1995)
- Chande, T.S. — Beyond Technical Analysis (John Wiley & Sons, 1995)
- PineScript reference:
aroonosc.pinein indicator directory