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Miha Kralj
59 lines
2.5 KiB
Markdown
59 lines
2.5 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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| Metric | Score | Notes |
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| :--- | :--- | :--- |
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| **Throughput** | 10 | High; O(1) calculation via cascaded SMAs. |
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| **Allocations** | 0 | Zero-allocation in hot paths. |
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| **Complexity** | O(1) | Constant time regardless of period. |
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| **Accuracy** | 10 | Matches TA-Lib exactly. |
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| **Timeliness** | 2 | Significant lag; double smoothing delays signals. |
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| **Overshoot** | 0 | Never overshoots the input data range. |
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| **Smoothness** | 9 | Very smooth; triangular weighting suppresses noise. |
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## Validation
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| Library | Status | Notes |
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| :--- | :--- | :--- |
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| **TA-Lib** | ✅ | Matches `TA_TRIMA` exactly. |
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| **Skender** | ✅ | Matches composite `SMA(SMA)` logic. |
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| **Tulip** | ✅ | Matches `trima` exactly. |
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| **Ooples** | N/A | Not implemented. |
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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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