QuanTAlib/lib/trends/tema/Tema.md

TEMA: Triple Exponential Moving Average

What It Does

The Triple Exponential Moving Average (TEMA) is a technical indicator designed to smooth price data while virtually eliminating the lag associated with traditional moving averages. By combining a single, double, and triple Exponential Moving Average (EMA), TEMA creates a composite line that tracks price action with remarkable speed and accuracy.

Historical Context

Developed by Patrick Mulloy and introduced in his 1994 article "Smoothing Data with Faster Moving Averages" in Technical Analysis of Stocks & Commodities, TEMA was created alongside DEMA (Double EMA) to solve the persistent problem of lag in trend-following indicators. Mulloy's innovation was to use the lag inherent in multiple EMA calculations to estimate and subtract the total lag from the original signal.

How It Works

The Core Idea

TEMA is not just "an EMA of an EMA of an EMA" (which would be very slow). Instead, it uses a clever formula to cancel out lag:

• EMA_1 has some lag.
• EMA_2 (EMA of EMA) has roughly double the lag.
• EMA_3 (EMA of EMA of EMA) has roughly triple the lag.

By combining these terms with specific weights (3 \times EMA_1 - 3 \times EMA_2 + EMA_3), the lag terms cancel out, leaving a moving average that hugs the price closely.

Mathematical Foundation

TEMA = (3 \times EMA_1) - (3 \times EMA_2) + EMA_3

Where:

• EMA_1 = EMA(Price)
• EMA_2 = EMA(EMA_1)
• EMA_3 = EMA(EMA_2)

Implementation Details

Our implementation uses three internal EMA instances.

• Complexity: O(1) per update.
• Initialization: We use Hunter's method for initializing the underlying EMAs to ensure the TEMA starts with valid values as early as possible.

Configuration

Parameter	Default	Purpose	Adjustment Guidelines
Period	14	Lookback window	Short (5-10) for scalping; Medium (20-50) for swing trading.

Performance Profile

Operation	Complexity	Description
Streaming update	O(1)	3 EMA updates + scalar math
Bar correction	O(1)	Efficient state rollback
Batch processing	O(N)	Single pass through data
Memory footprint	O(1)	Stores state for 3 internal EMAs

Interpretation

Trading Signals

Trend Direction

• Fast Response: TEMA turns much faster than SMA or EMA. A turn in TEMA often precedes a turn in price trend.

Crossovers

• Price Crossover: Because TEMA hugs price so closely, crossovers are frequent. They are best used for short-term entries in the direction of a larger trend.

When It Works Best

• Momentum Trading: TEMA is excellent for capturing short-term bursts of momentum.

When It Struggles

• Overshoot: In a sudden V-shaped reversal, TEMA can "overshoot" the price briefly due to the momentum of its internal calculation components.

Architecture Notes

This implementation makes specific trade-offs:

Choice: Composition

• Implementation: Composed of 3 Ema objects.
• Rationale: Reusing the robust Ema class ensures consistent behavior (like initialization and NaN handling) across the library.

References

• Mulloy, Patrick G. "Smoothing Data with Faster Moving Averages." Technical Analysis of Stocks & Commodities, Jan 1994.

C# Usage

Streaming Updates (Single Instance)

using QuanTAlib;

var tema = new Tema(period: 14);

// Process each new bar
TValue result = tema.Update(new TValue(timestamp, closePrice));
Console.WriteLine($"TEMA: {result.Value:F2}");

// Check if buffer is full
if (tema.IsHot)
{
    // Indicator is fully initialized
}

Batch Processing (Historical Data)

// TSeries API
TSeries prices = ...;
TSeries temaValues = Tema.Batch(prices, period: 14);

// Span API (High Performance)
double[] prices = new double[1000];
double[] output = new double[1000];
Tema.Calculate(prices.AsSpan(), output.AsSpan(), period: 14);

Bar Correction (isNew Parameter)

var tema = new Tema(14);

// New bar
tema.Update(new TValue(time, 100), isNew: true);

// Intra-bar update
tema.Update(new TValue(time, 101), isNew: false); // Replaces 100 with 101