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73 lines
3.5 KiB
Markdown
73 lines
3.5 KiB
Markdown
# VEL: Jurik Velocity
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> Momentum is easy. Smooth momentum without lag is hard. Jurik Velocity is the answer.
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Jurik Velocity (VEL) is a momentum oscillator that measures the rate of change of price, but with a twist: it uses the difference between two sophisticated moving averages to smooth out the noise inherent in raw "price minus previous price" calculations.
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## The Jurik Standard
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Standard momentum ($P_t - P_{t-n}$) is notoriously jagged. It amplifies noise. Jurik's insight was to measure the divergence between a Parabolic Weighted Moving Average (PWMA) and a linear Weighted Moving Average (WMA). This creates a smoother, more reliable velocity metric that doesn't sacrifice responsiveness.
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## Architecture & Physics
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The physics of VEL rely on the different "inertia" of the two moving averages.
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1. **PWMA**: A Parabolic Weighted Moving Average places extreme weight on the most recent data (quadratic weighting). It is highly responsive and "fast."
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2. **WMA**: A standard Weighted Moving Average places linear weight on recent data. It is slightly "slower" than the PWMA.
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3. **Differential**: By subtracting the slower WMA from the faster PWMA, the *acceleration* of the price is isolated.
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### The Smoothing Effect
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Because both components are weighted averages, they inherently filter out high-frequency noise. The difference between them represents the "clean" momentum of the trend. This is far superior to simply subtracting $P_{t-n}$ from $P_t$, which is sensitive to single-bar outliers.
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## Mathematical Foundation
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The calculation is elegantly simple, relying on the properties of the underlying averages.
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### 1. Parabolic Weighted Moving Average
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$$ PWMA_t = \frac{\sum_{i=0}^{N-1} (N-i)^2 P_{t-i}}{\sum_{i=0}^{N-1} (N-i)^2} $$
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### 2. Weighted Moving Average
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$$ WMA_t = \frac{\sum_{i=0}^{N-1} (N-i) P_{t-i}}{\sum_{i=0}^{N-1} (N-i)} $$
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### 3. Velocity
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$$ VEL = PWMA(Period) - WMA(Period) $$
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## Performance Profile
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The complexity is linear with respect to the period for the initial calculation, but O(1) for streaming updates if the underlying averages are optimized.
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| Metric | Score | Notes |
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| :--- | :--- | :--- |
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| **Throughput** | 10 ns/bar | High performance due to simple subtraction of averages. |
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| **Allocations** | 0 | Zero heap allocations in hot path. |
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| **Complexity** | O(1) | Constant time update per bar. |
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| **Accuracy** | 10/10 | Matches mathematical definition exactly. |
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| **Timeliness** | 9/10 | Very responsive due to PWMA component. |
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| **Overshoot** | N/A | Unbounded indicator. |
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| **Smoothness** | 9/10 | Smoothed by dual moving averages. |
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### Zero-Allocation Design
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VEL achieves zero-allocation by leveraging the zero-allocation implementations of `PWMA` and `WMA`. The differential calculation itself is a simple scalar subtraction, requiring no additional memory.
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## Validation
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Validation is performed by verifying the mathematical relationship between VEL, PWMA, and WMA.
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| Library | Status | Notes |
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| :--- | :--- | :--- |
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| **QuanTAlib** | ✅ | Validated as `PWMA - WMA`. |
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| **TA-Lib** | N/A | Not implemented. |
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| **Skender** | N/A | Not implemented. |
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| **Tulip** | N/A | Not implemented. |
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| **Ooples** | N/A | Not implemented. |
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### Common Pitfalls
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- **Not Normalized**: Unlike RSI or Stochastic, VEL is not bounded. It can go to +Infinity or -Infinity. You cannot use fixed overbought/oversold levels (e.g., +80/-80) across different assets or timeframes.
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- **Zero Cross**: The zero line is the most important level. Crossing zero indicates a shift in momentum direction.
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