QuanTAlib/lib/trends/trima/Trima.md

TRIMA: Triangular Moving Average

"The weighted blanket of moving averages. It doesn't care where the price is going right now; it cares where the price feels most comfortable."

The Triangular Moving Average (TRIMA) places the majority of its weight on the middle of the data window, tapering off linearly towards the ends. This creates a triangular weight distribution (hence the name). It is mathematically equivalent to a double-smoothed SMA.

Historical Context

TRIMA has been a staple in cycle analysis. By double-smoothing the data, it effectively removes high-frequency noise, making it ideal for identifying dominant market cycles. However, this smoothness comes at the cost of significant lag.

Architecture & Physics

TRIMA is implemented as a cascade of two Simple Moving Averages.

TRIMA = SMA(SMA(Price, P_1), P_2)

Where P_1 and P_2 are roughly half the total period.

The Weight Distribution

An SMA has a rectangular weight distribution (all weights equal). A WMA has a linear distribution (heaviest at the end). TRIMA has a triangular distribution (heaviest in the center).

Mathematical Foundation

1. Period Splitting

P_1 = \lfloor \frac{N}{2} \rfloor + 1 P_2 = \lceil \frac{N+1}{2} \rceil

2. The Cascade

TRIMA = SMA(SMA(Price, P_1), P_2)

Performance Profile

Metric	Score	Notes
Throughput	10	High; O(1) calculation via cascaded SMAs.
Allocations	0	Zero-allocation in hot paths.
Complexity	O(1)	Constant time regardless of period.
Accuracy	10	Matches TA-Lib exactly.
Timeliness	2	Significant lag; double smoothing delays signals.
Overshoot	0	Never overshoots the input data range.
Smoothness	9	Very smooth; triangular weighting suppresses noise.

Validation

Library	Status	Notes
TA-Lib	✅	Matches TA_TRIMA exactly.
Skender	✅	Matches composite SMA(SMA) logic.
Tulip	✅	Matches trima exactly.
Ooples	N/A	Not implemented.

Common Pitfalls

1. Lag: TRIMA has more lag than SMA, EMA, or WMA. It is a lagging indicator, not a leading one.
2. Signal Generation: Due to its lag, TRIMA is poor for crossover signals. It is best used for visual trend identification or as a baseline for envelopes (e.g., TMA Bands).
3. Even/Odd Periods: The exact calculation of P_1 and P_2 differs slightly between implementations for even periods. QuanTAlib matches the standard definition used by TA-Lib.