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.
4.8 KiB
AMAT: Archer Moving Averages Trends
The Archer Moving Averages Trends indicator is a triple-confirmation trend identification system that uses dual EMAs to produce discrete directional signals (+1 bullish, -1 bearish, 0 neutral). Unlike simple crossover systems that trigger on any intersection, AMAT requires alignment of three conditions: relative position (fast above/below slow), fast EMA direction (rising/falling), and slow EMA direction (rising/falling). This triple gate filters out the whipsaw endemic to single-condition crossover systems in ranging markets. A secondary output quantifies trend strength as the percentage separation between EMAs, providing a conviction metric for position sizing.
Historical Context
AMAT emerged from concepts attributed to Mark Whistler ("Archer" in trading circles) and was formalized by Tom Joseph in 2009. The indicator addresses a specific failure mode of traditional MA crossover systems: they generate excessive false signals during sideways markets because a crossover only measures relative position, not directional agreement. A fast EMA can cross above a slow EMA while both are falling — technically a "bullish crossover" but practically meaningless. AMAT's innovation is requiring all three conditions to align before committing to a directional call. The neutral state (output = 0) captures market indecision explicitly: when EMAs disagree on direction or their relative position contradicts their momentum, AMAT stays flat. Markets trend roughly 30% of the time. AMAT is designed to identify that 30% with high confidence and stay silent the other 70%.
Architecture & Physics
1. Dual EMA Computation
Two independent EMAs with bias compensation during warmup:
\text{EMA}_t = \alpha \cdot P_t + (1 - \alpha) \cdot \text{EMA}_{t-1}
where \alpha = \frac{2}{N + 1}
Bias compensation removes initialization distortion:
e_t = e_{t-1} \times (1 - \alpha), \quad \text{EMA}_{\text{comp}} = \frac{\text{EMA}_t}{1 - e_t}
2. Direction Detection
\text{Dir}_t = \begin{cases} +1 & \text{if } \text{EMA}_t > \text{EMA}_{t-1} \\ -1 & \text{if } \text{EMA}_t < \text{EMA}_{t-1} \\ 0 & \text{otherwise} \end{cases}
3. Triple-Confirmation Logic
\text{Trend}_t = \begin{cases} +1 & \text{if Fast} > \text{Slow} \;\land\; \text{FastDir} = +1 \;\land\; \text{SlowDir} = +1 \\ -1 & \text{if Fast} < \text{Slow} \;\land\; \text{FastDir} = -1 \;\land\; \text{SlowDir} = -1 \\ 0 & \text{otherwise} \end{cases}
4. Trend Strength
\text{Strength}_t = \frac{|\text{Fast}_t - \text{Slow}_t|}{\text{Slow}_t} \times 100
5. Complexity
- Time:
O(1)per bar — two EMA updates plus comparisons - Space:
O(1)— scalar state only - Warmup: slowPeriod bars
Mathematical Foundation
Parameters
| Symbol | Parameter | Default | Constraint |
|---|---|---|---|
N_f |
fastPeriod | 10 | N_f \geq 1 |
N_s |
slowPeriod | 50 | N_s > N_f |
Pseudo-code
Initialize:
α_fast = 2 / (fastPeriod + 1)
α_slow = 2 / (slowPeriod + 1)
ema_fast = ema_slow = 0
e_fast = e_slow = 1.0
prev_fast = prev_slow = 0
bar_count = 0
On each bar (price, isNew):
if !isNew: restore previous state
// EMA updates
ema_fast = FMA(ema_fast, 1 - α_fast, α_fast × price)
e_fast = e_fast × (1 - α_fast)
fast = ema_fast / (1 - e_fast)
ema_slow = FMA(ema_slow, 1 - α_slow, α_slow × price)
e_slow = e_slow × (1 - α_slow)
slow = ema_slow / (1 - e_slow)
// Direction detection
fastDir = fast > prev_fast ? +1 : fast < prev_fast ? -1 : 0
slowDir = slow > prev_slow ? +1 : slow < prev_slow ? -1 : 0
// Triple-confirmation
if fast > slow AND fastDir == +1 AND slowDir == +1:
trend = +1
else if fast < slow AND fastDir == -1 AND slowDir == -1:
trend = -1
else:
trend = 0
// Strength
strength = slow > 0 ? |fast - slow| / slow × 100 : 0
prev_fast = fast
prev_slow = slow
output:
Trend = trend // +1, -1, or 0
Strength = strength // percentage
Period Selection Guidelines
| Use Case | Fast | Slow | Ratio |
|---|---|---|---|
| Scalping | 5 | 13 | 1:2.6 |
| Swing | 10 | 50 | 1:5 |
| Position | 20 | 100 | 1:5 |
| Investment | 50 | 200 | 1:4 |
Fast periods too close to slow periods produce excessive neutral readings. A ratio of 1:4 to 1:5 provides effective separation.
Discrete Output Properties
- +1: All three conditions align bullish — high-confidence uptrend
- -1: All three conditions align bearish — high-confidence downtrend
- 0: Any disagreement — indeterminate; no position recommended
- Strength: Quantifies EMA separation as percentage of slow EMA; useful for position sizing but not directional signal
Resources
- Joseph, T. — AMAT trend confirmation methodology (2009)
- PineScript reference:
amat.pinein indicator directory