QuanTAlib/lib/dynamics/amat/Amat.md

AMAT: Archer Moving Averages Trends

"Markets trend about 30% of the time. The trick isn't just finding trends—it's confirming them before your stops get hit."

AMAT (Archer Moving Averages Trends) is a trend identification system that uses dual EMAs to provide clear directional signals. Unlike simple moving average crossovers that generate signals on any intersection, AMAT requires alignment of both fast and slow averages moving in the same direction—reducing false signals during choppy, sideways markets.

Historical Context

AMAT emerged from concepts developed by Mark Whistler (known as "Archer" in trading circles) and was formalized by Tom Joseph in 2009. The indicator addresses a fundamental problem with traditional crossover systems: they generate excessive whipsaws in ranging markets because a crossover only measures relative position, not directional agreement.

The innovation lies in requiring three conditions for a trend signal:

1. Relative position (fast above/below slow)
2. Fast EMA direction (rising/falling)
3. Slow EMA direction (rising/falling)

This triple-confirmation approach filters out the noise inherent in single-condition systems.

Architecture & Physics

AMAT operates on dual EMA calculations with directional analysis. The computational flow:

Input Price
    │
    ├──► Fast EMA ───► Direction (rising/falling)
    │                         │
    │                         ▼
    └──► Slow EMA ───► Direction (rising/falling)
                              │
                              ▼
                    Trend Logic (+1, -1, 0)
                              │
                              ▼
                    Strength = |Fast - Slow| / Slow × 100

Trend State Machine

State	Fast vs Slow	Fast Direction	Slow Direction
Bullish (+1)	Fast > Slow	Rising	Rising
Bearish (-1)	Fast < Slow	Falling	Falling
Neutral (0)	Any	Mixed	Mixed

The neutral state captures market indecision: when EMAs disagree on direction or their relative position contradicts their momentum, AMAT stays flat. This is a feature, not a limitation.

EMA Bias Compensation

QuanTAlib's implementation uses bias-compensated EMAs during the warmup phase. Traditional EMA initialization assumes the first price equals the true average—a convenient fiction. The compensator factor e decays exponentially:

e_{t} = e_{t-1} \times (1 - \alpha)

Until convergence, the EMA is divided by (1 - e) to remove initialization bias.

Mathematical Foundation

1. EMA Calculation

\text{EMA}_t = \alpha \times P_t + (1 - \alpha) \times \text{EMA}_{t-1}

Where \alpha = \frac{2}{n + 1} and n is the period.

2. Direction Detection

\text{Direction}_t = \begin{cases} \text{rising} & \text{if } \text{EMA}_t > \text{EMA}_{t-1} \\ \text{falling} & \text{if } \text{EMA}_t < \text{EMA}_{t-1} \\ \text{flat} & \text{otherwise} \end{cases}

3. Trend Signal

\text{Trend}_t = \begin{cases} +1 & \text{if } \text{FastEMA}_t > \text{SlowEMA}_t \land \text{FastRising} \land \text{SlowRising} \\ -1 & \text{if } \text{FastEMA}_t < \text{SlowEMA}_t \land \text{FastFalling} \land \text{SlowFalling} \\ 0 & \text{otherwise} \end{cases}

4. Trend Strength

\text{Strength}_t = \frac{|\text{FastEMA}_t - \text{SlowEMA}_t|}{\text{SlowEMA}_t} \times 100

Strength quantifies the separation between EMAs as a percentage of the slow EMA—useful for gauging trend conviction or filtering weak signals.

Usage

// Standard instantiation
var amat = new Amat(fastPeriod: 10, slowPeriod: 50);

// Process streaming data
foreach (var price in prices)
{
    amat.Update(new TValue(DateTime.UtcNow, price));

    if (amat.Last.Value == 1.0)
        Console.WriteLine($"Bullish - Strength: {amat.Strength.Value:F2}%");
    else if (amat.Last.Value == -1.0)
        Console.WriteLine($"Bearish - Strength: {amat.Strength.Value:F2}%");
    else
        Console.WriteLine("Neutral");
}

// Access individual EMAs
double fastEma = amat.FastEma.Value;
double slowEma = amat.SlowEma.Value;

// Batch processing
var results = Amat.Batch(priceSeries, fastPeriod: 10, slowPeriod: 50);

// Span-based high-performance
double[] trend = new double[prices.Length];
double[] strength = new double[prices.Length];
Amat.Calculate(prices.AsSpan(), trend, strength, fastPeriod: 10, slowPeriod: 50);

Event-Driven (Chained)

var source = new TSeries();
var amat = new Amat(source, fastPeriod: 10, slowPeriod: 50);

// AMAT automatically updates when source publishes
source.Add(new TValue(DateTime.UtcNow, 100.0));
Console.WriteLine($"Trend: {amat.Last.Value}");

Parameters

Parameter	Type	Default	Description
fastPeriod	int	10	Fast EMA period (must be > 0)
slowPeriod	int	50	Slow EMA period (must be > fastPeriod)

Common Period Combinations

Use Case	Fast	Slow	Notes
Scalping	5	13	High responsiveness, more signals
Swing	10	50	Balanced, classic configuration
Position	20	100	Filtered for major trends
Investment	50	200	Long-term directional bias

Output Properties

Property	Type	Description
Last	TValue	Trend direction: +1 (bullish), -1 (bearish), 0 (neutral)
Strength	TValue	Trend strength as percentage
FastEma	TValue	Current fast EMA value
SlowEma	TValue	Current slow EMA value
IsHot	bool	True when both EMAs are fully warmed
WarmupPeriod	int	Equal to slowPeriod

Performance Profile

Metric	Score	Notes
Throughput	~15 ns/bar	Dual EMA + direction check
Allocations	0	Streaming mode is allocation-free
Complexity	O(1)	Constant time per update
Accuracy	9/10	Bias-compensated EMAs match external libs
Timeliness	7/10	Triple-confirmation adds slight lag
Overshoot	8/10	No overshoot; discrete {-1, 0, +1} output
Smoothness	6/10	State transitions can be abrupt

Validation

AMAT is a custom indicator not present in standard TA libraries. Validation confirms:

Component	Library	Status	Notes
Fast EMA	TA-Lib	✅	Matches TA_EMA
Fast EMA	Skender	✅	Matches GetEma
Slow EMA	TA-Lib	✅	Matches TA_EMA
Slow EMA	Skender	✅	Matches GetEma
Trend Logic	Manual	✅	Verified against known patterns
Strength	Manual	✅	Formula verification

Common Pitfalls

1. Expecting Continuous Signals

AMAT returns 0 (neutral) frequently. This is intentional—choppy markets produce neutral signals. Trading systems should respect neutral states rather than forcing a directional bias.

2. Period Selection

Fast periods that are too close to slow periods produce excessive neutral readings. A ratio of 1:5 (e.g., 10/50) provides reasonable separation.

3. Strength Interpretation

High strength doesn't guarantee trend continuation. It measures current separation, not momentum. A declining strength during a +1 trend may indicate weakening conviction.

4. Initialization Phase

Until IsHot returns true, trend signals may be unreliable. The indicator needs slowPeriod bars to stabilize both EMAs.

See Also

• EMA - Exponential Moving Average (AMAT's building block)
• MACD - Another dual-EMA system with different logic
• ADX - Trend strength without directional bias