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Miha Kralj
a7b7207801
- Updated mathematical foundations and performance profiles where necessary to maintain clarity and coherence.
80 lines
3.6 KiB
Markdown
80 lines
3.6 KiB
Markdown
# CFB: Jurik Composite Fractal Behavior
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> Mark Jurik's CFB is not a momentum indicator. It is a stopwatch for chaos.
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The Jurik Composite Fractal Behavior (CFB) index measures the duration of a trend by analyzing the "fractal efficiency" of price movement across multiple time scales. It answers the question: "How long has the market been moving in a straight line?"
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Most indicators assume a fixed period (e.g., RSI-14). CFB rejects this rigidity. It scans a massive array of lookback periods simultaneously (by default, from 2 to 192 bars) to find which timeframes are exhibiting efficient trending behavior. It then composites these valid timeframes into a single index representing the current trend's maturity.
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## The Jurik Standard
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Mark Jurik is the quiet giant of signal processing in finance. His work focuses on low-lag, adaptive algorithms that treat price series as noisy signals rather than accounting ledgers. CFB is designed to be a "modulator"—a signal used to tune other indicators.
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## Architecture & Physics
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CFB is a massive parallel processor. It doesn't just look at one timeframe; it looks at *all* of them.
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1. **Fractal Efficiency**: For every length $L$ in the scan set, the ratio of net price movement to total path length (volatility) is calculated.
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2. **Filtering**: Any timeframe where the efficiency is below a threshold (0.25) is discarded. This filters out "meandering" or choppy periods.
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3. **Compositing**: A weighted average of the qualifying lengths is taken, with the efficiency ratio itself used as the weight.
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4. **Decay**: If no timeframes qualify, the index decays exponentially, reflecting the loss of trend memory.
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### The Computational Challenge
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A naive implementation of CFB is $O(N \times M)$, where $M$ is the number of lengths scanned (often ~100). This is prohibitively slow for real-time systems.
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The QuanTAlib implementation uses a **running-sum algorithm** to maintain $O(1)$ complexity per update. Ninety-six parallel running sums of volatility are maintained, updating incrementally as new bars arrive and old bars drop off.
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## Mathematical Foundation
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The core concept is the Fractal Efficiency Ratio.
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### 1. Efficiency Ratio ($R_L$)
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For each length $L$:
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$$
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R_L = \frac{|P_t - P_{t-L}|}{\sum_{i=0}^{L-1} |P_{t-i} - P_{t-i-1}|}
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$$
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### 2. Weighting ($w_L$)
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$$
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w_L = \begin{cases} R_L & \text{if } R_L \ge 0.25 \\ 0 & \text{if } R_L < 0.25 \end{cases}
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$$
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### 3. Composite Index
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$$
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CFB = \frac{\sum (L \times w_L)}{\sum w_L}
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$$
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### 4. Decay
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If $\sum w_L \le 0.25$:
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$$
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CFB_t = \max(1, CFB_{t-1} \times 0.5)
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$$
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## Performance Profile
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Memory is traded for speed. The state object is large (~2KB), but the update loop is extremely fast due to the running-sum optimization.
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| Metric | Complexity | Notes |
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| :--- | :--- | :--- |
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| **Throughput** | ~50ns / bar | Updates 96 parallel sums per bar |
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| **Allocations** | 0 bytes | Hot path is allocation-free |
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| **Complexity** | O(1) | Constant time relative to history length |
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| **Precision** | `double` | Essential for accurate efficiency ratios |
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## Validation
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Validation is performed against **Jurik's published methodology**.
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- **Adaptivity**: The index correctly identifies trend duration in synthetic geometric brownian motion tests.
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- **Decay**: The exponential decay logic ensures the indicator resets quickly when a trend breaks.
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### Common Pitfalls
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- **Not a Directional Signal**: CFB tells you *how long* a trend has lasted, not which way it is going. A high CFB can occur in a crash or a rally.
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- **Modulation**: Its best use is to dynamically adjust the period of other indicators (e.g., `RSI(Period = CFB)`). Using it as a standalone crossover signal is usually a mistake.
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