QuanTAlib/lib/dynamics/amat/Amat.md

AMAT: Archer Moving Averages Trends

Archer's moving average trends compare fast and slow averages, signaling when short-term momentum confirms the longer-term direction.

Property	Value
Category	Dynamic
Inputs	OHLCV bar (TBar)
Parameters	fastPeriod (default 10), slowPeriod (default 50)
Outputs	Multiple series (Strength, FastEma, SlowEma)
Output range	Varies (see docs)
Warmup	slowPeriod bars
PineScript	amat.pine

• The Archer Moving Averages Trends indicator is a triple-confirmation trend identification system that uses dual EMAs to produce discrete directiona...
• Similar: Alligator, Ichimoku | Complementary: ADX for trend strength | Trading note: Archer Moving Average Trend; uses MA crossover zones to classify trend phases.
• Validated against TA-Lib, Skender, and Tulip reference implementations where available.

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

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

Performance Profile

Operation Count (Streaming Mode)

AMAT compares a fast EMA against a slow EMA to determine trend direction.

Post-warmup steady state (per bar):

Operation	Count	Cost (cycles)	Subtotal
FMA × 2 (fast EMA, slow EMA updates)	2	4	8
CMP (fast > slow → trend = 1 else 0)	1	1	1
Total	3	—	~9 cycles

Two independent EMA streams with a single comparison. One of the cheapest dynamics indicators: ~9 cycles per bar at steady state.

Batch Mode (SIMD Analysis)

Operation	Vectorizable?	Notes
EMA (fast)	No	Recursive IIR — sequential
EMA (slow)	No	Recursive IIR — sequential
Comparison	Yes	VCMPPD after both EMA arrays computed

Both EMA passes are recursive and sequential. The final comparison step is trivially vectorizable once both arrays exist.

Quality Metrics

Metric	Score	Notes
Accuracy	9/10	Exact EMA arithmetic; binary output eliminates rounding nuance
Timeliness	7/10	Slow EMA period determines lag; faster than SMA-based versions
Smoothness	10/10	Binary 0/1 output is maximally smooth by definition
Noise Rejection	7/10	EMA crossover can whipsaw in sideways markets

Resources

• Joseph, T. — AMAT trend confirmation methodology (2009)
• PineScript reference: amat.pine in indicator directory