QuanTAlib/lib/trends/trima/Trima.md

TRIMA: Triangular Moving Average

What It Does

The Triangular Moving Average (TRIMA) is a weighted moving average where the weights are assigned in a triangular pattern. The most recent data and the oldest data carry the least weight, while the data in the middle of the period carries the most weight. This creates a double-smoothing effect that produces a line much smoother than a Simple Moving Average (SMA) or Exponential Moving Average (EMA), making it ideal for identifying the primary trend without the distraction of short-term noise.

Historical Context

While the concept of triangular weighting has roots in statistical signal processing, it was popularized in technical analysis as a way to solve the "whipsaw" problem of SMAs. By de-emphasizing the most recent data (which is often noisy), TRIMA focuses on the "consensus" of value over the period.

How It Works

The Core Idea

TRIMA is mathematically equivalent to a "double SMA."

• SMA: Average of N prices.
• TRIMA: Average of an Average. Specifically, an SMA of period X applied to an SMA of period X.

Because it averages an average, it is extremely smooth. However, this double smoothing comes at the cost of increased lag. It will turn significantly later than an EMA or SMA.

Mathematical Foundation

The weights form a triangle. For a period of 5:

• Weights: 1, 2, 3, 2, 1
• Sum of weights: 1+2+3+2+1 = 9

Formula:

TRIMA = \frac{\sum (Price_i \times Weight_i)}{\sum Weights}

Equivalent Calculation (Double SMA):

TRIMA(N) \approx SMA(SMA(Price, \lceil N/2 \rceil), \lfloor N/2 \rfloor + 1)

Implementation Details

Our implementation uses the Double SMA method for O(1) efficiency.

• Complexity: O(1) per update (two sliding window sums).
• Stability: Inherits the stability of SMA.

Configuration

Parameter	Default	Purpose	Adjustment Guidelines
Period	14	Lookback window	Standard lookback.

Performance Profile

Operation	Complexity	Description
Streaming update	O(1)	Two sliding window sums
Bar correction	O(1)	Efficient state rollback
Batch processing	O(N)	Single pass through data
Memory footprint	O(period)	RingBuffers for the two internal SMAs

Interpretation

Trading Signals

Trend Identification

• Primary Trend: TRIMA is excellent for visualizing the "major" trend. If TRIMA is rising, the long-term direction is up, regardless of short-term chops.

When It Works Best

• Visual Clarity: Traders often use TRIMA not for signals, but to declutter charts and see the underlying market structure.

When It Struggles

• Timing Entries: Due to its significant lag, TRIMA is poor for timing entries or exits. It is a lagging indicator, not a leading one.

Architecture Notes

This implementation makes specific trade-offs:

Choice: Double SMA Composition

• Implementation: Composed of two Sma objects.
• Rationale: This is mathematically equivalent to the weighted sum method but allows us to reuse the O(1) optimization of the Sma class.

References

• Merrill, Arthur A. "Filtered Waves." Technical Analysis of Stocks & Commodities.

C# Usage

Streaming Updates (Single Instance)

using QuanTAlib;

var trima = new Trima(period: 14);

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

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

Batch Processing (Historical Data)

// TSeries API
TSeries prices = ...;
TSeries trimaValues = Trima.Batch(prices, period: 14);

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

Bar Correction (isNew Parameter)

var trima = new Trima(14);

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

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