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Miha Kralj
a7b7207801
- Updated mathematical foundations and performance profiles where necessary to maintain clarity and coherence.
44 lines
1.9 KiB
Markdown
44 lines
1.9 KiB
Markdown
# TRIMA: Triangular Moving Average
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> "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."
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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.
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## Historical Context
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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.
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## Architecture & Physics
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TRIMA is implemented as a cascade of two Simple Moving Averages.
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$$ TRIMA = SMA(SMA(Price, P_1), P_2) $$
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Where $P_1$ and $P_2$ are roughly half the total period.
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### The Weight Distribution
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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).
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## Mathematical Foundation
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### 1. Period Splitting
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$$ P_1 = \lfloor \frac{N}{2} \rfloor + 1 $$
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$$ P_2 = \lceil \frac{N+1}{2} \rceil $$
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### 2. The Cascade
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$$ TRIMA = SMA(SMA(Price, P_1), P_2) $$
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## Performance Profile
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## Validation
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Validated against TA-Lib (`TA_TRIMA`) and Skender.Stock.Indicators.
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### Common Pitfalls
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1. **Lag**: TRIMA has more lag than SMA, EMA, or WMA. It is a lagging indicator, not a leading one.
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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).
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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.
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