3.2 KiB
JMA: Jurik Moving Average
"The Ferrari of moving averages. Fast, smooth, and expensive (computationally). It tracks price like a heat-seeking missile."
JMA (Jurik Moving Average) is widely considered the gold standard for adaptive smoothing. Developed by Mark Jurik, it offers an unparalleled combination of noise reduction and minimal lag. It achieves this through a complex, multi-stage algorithm that adapts its internal parameters based on the fractal dimension and volatility of the data.
Historical Context
Mark Jurik kept the JMA algorithm a trade secret for years. It was sold as a "black box" library. Eventually, reverse-engineered versions appeared, revealing a sophisticated mix of volatility-adjusted smoothing and Kalman-like filtering. Our implementation is based on these high-fidelity reconstructions.
Architecture & Physics
JMA is not a simple FIR or IIR filter. It's a dynamic system.
- Volatility Assessment: It calculates a 10-bar SMA of local deviation and compares it to a 128-bar volatility history (using a trimmed mean).
- Fractal Efficiency: It computes a dynamic exponent based on the ratio of current change to historical volatility.
- Adaptive Smoothing: It uses this exponent to drive a 2-pole IIR filter that speeds up when the market moves and slows down when it chops.
Zero-Allocation Design
We've ported the complex logic to a zero-allocation C# implementation.
- RingBuffers: Used for the volatility history (128 bars) and deviation (10 bars).
- Trimmed Mean: We use a pre-allocated sort buffer to calculate the trimmed mean without heap allocations.
- State Management: All internal state (bands, IIR coefficients) is preserved in a
struct.
Mathematical Foundation
The core update logic involves a dynamic alpha \alpha:
\text{Ratio} = \frac{\text{AbsDiff}}{\text{Volatility}}
d = \text{Ratio}^{\text{Power}}
\alpha = \text{LengthDivider}^d
\text{JMA}_t = (1 - \alpha) P_t + \alpha \text{JMA}_{t-1} + \dots
(The full formula involves multiple feedback loops and phase adjustments).
Performance Profile
JMA is computationally expensive compared to an EMA, but still fast enough for real-time use.
| Metric | Score | Notes |
|---|---|---|
| Throughput | Low | Complex algorithm |
| Complexity | O(1) | Constant time update |
| Accuracy | 9/10 | Tracks price action with high fidelity |
| Timeliness | 9/10 | Minimal lag due to adaptive phase |
| Overshoot | 8/10 | Controlled overshoot, adjustable via phase |
| Smoothness | 9/10 | Exceptional noise reduction |
Validation
Validated against known JMA outputs from other platforms (e.g., AmiBroker, NinjaTrader).
| Provider | Error Tolerance | Notes |
|---|---|---|
| Reverse Eng. | 10^{-6} |
Matches standard decompiled logic |
Common Pitfalls
- Phase Parameter: The
phaseparameter controls overshoot. Positive values (up to 100) make it overshoot like a DEMA. Negative values make it lag more but smoother. 0 is neutral. - Warmup: JMA needs a long warmup (65+ bars) to build its volatility history. Do not trust the first 100 bars.
- Complexity: This is the most complex moving average in the library. If you need simple, use EMA. If you need magic, use JMA.