3.2 KiB
VEL: Jurik Velocity
Momentum is easy. Smooth momentum without lag is hard. Jurik Velocity is the answer.
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.
The Jurik Standard
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.
Architecture & Physics
The physics of VEL rely on the different "inertia" of the two moving averages.
- PWMA: A Parabolic Weighted Moving Average places extreme weight on the most recent data (quadratic weighting). It is highly responsive and "fast."
- WMA: A standard Weighted Moving Average places linear weight on recent data. It is slightly "slower" than the PWMA.
- Differential: By subtracting the slower WMA from the faster PWMA, we isolate the acceleration of the price.
The Smoothing Effect
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.
Zero-Allocation Design
The implementation leverages existing Pwma and Wma classes. The Update method is allocation-free. For batch processing, we use stackalloc for intermediate buffers when the dataset is small (<= 1024 bars), ensuring zero GC pressure.
Mathematical Foundation
The calculation is elegantly simple, relying on the properties of the underlying averages.
1. Parabolic Weighted Moving Average
PWMA_t = \frac{\sum_{i=0}^{N-1} (N-i)^2 P_{t-i}}{\sum_{i=0}^{N-1} (N-i)^2}
2. Weighted Moving Average
WMA_t = \frac{\sum_{i=0}^{N-1} (N-i) P_{t-i}}{\sum_{i=0}^{N-1} (N-i)}
3. Velocity
VEL = PWMA(Period) - WMA(Period)
Performance Profile
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.
| Metric | Complexity | Notes |
|---|---|---|
| Throughput | ~10ns / bar | Dependent on underlying MA performance |
| Allocations | 0 bytes | Hot path is allocation-free |
| Complexity | O(1) | Constant time per update |
| Precision | double |
Standard floating-point precision |
Validation
We validate against Jurik's published methodology.
- Smoothness: VEL is significantly smoother than raw ROC or Momentum indicators.
- Responsiveness: Despite the smoothing, VEL leads simple moving average crossovers.
Common Pitfalls
- 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.
- Zero Cross: The zero line is the most important level. Crossing zero indicates a shift in momentum direction.