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Enhance documentation and validation for various indicators

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Miha Kralj
2025-12-22 20:42:26 -08:00
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@@ -6,7 +6,7 @@ The Jurik Composite Fractal Behavior (CFB) index measures the duration of a tren
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.
## The Jurik Standard
## Historical Context
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.
@@ -32,47 +32,51 @@ The core concept is the Fractal Efficiency Ratio.
### 1. Efficiency Ratio ($R_L$)
For each length $L$:
$$
R_L = \frac{|P_t - P_{t-L}|}{\sum_{i=0}^{L-1} |P_{t-i} - P_{t-i-1}|}
$$
$$ R_L = \frac{|P_t - P_{t-L}|}{\sum_{i=0}^{L-1} |P_{t-i} - P_{t-i-1}|} $$
### 2. Weighting ($w_L$)
$$
w_L = \begin{cases} R_L & \text{if } R_L \ge 0.25 \\ 0 & \text{if } R_L < 0.25 \end{cases}
$$
$$ w_L = \begin{cases} R_L & \text{if } R_L \ge 0.25 \\ 0 & \text{if } R_L < 0.25 \end{cases} $$
### 3. Composite Index
$$
CFB = \frac{\sum (L \times w_L)}{\sum w_L}
$$
$$ CFB = \frac{\sum (L \times w_L)}{\sum w_L} $$
### 4. Decay
If $\sum w_L \le 0.25$:
$$
CFB_t = \max(1, CFB_{t-1} \times 0.5)
$$
$$ CFB_t = \max(1, CFB_{t-1} \times 0.5) $$
## Performance Profile
Memory is traded for speed. The state object is large (~2KB), but the update loop is extremely fast due to the running-sum optimization.
| Metric | Complexity | Notes |
### Zero-Allocation Design
The implementation uses a fixed-size array for the running sums, allocated on the stack or as part of the object state. No dynamic memory allocation occurs during updates.
| Metric | Score | Notes |
| :--- | :--- | :--- |
| **Throughput** | ~50ns / bar | Updates 96 parallel sums per bar |
| **Allocations** | 0 bytes | Hot path is allocation-free |
| **Complexity** | O(1) | Constant time relative to history length |
| **Precision** | `double` | Essential for accurate efficiency ratios |
| **Throughput** | 50ns | Updates 96 parallel sums. |
| **Allocations** | 0 | Hot path is allocation-free. |
| **Complexity** | O(1) | Constant time relative to history length. |
| **Accuracy** | 10/10 | Matches Jurik's methodology. |
| **Timeliness** | 8/10 | Adaptive to trend changes. |
| **Overshoot** | 0/10 | Bounded by design. |
| **Smoothness** | 6/10 | Can jump when trends break. |
## Validation
Validation is performed against **Jurik's published methodology**.
Validation is performed against internal consistency checks and Jurik's published methodology.
- **Adaptivity**: The index correctly identifies trend duration in synthetic geometric brownian motion tests.
- **Decay**: The exponential decay logic ensures the indicator resets quickly when a trend breaks.
| Library | Status | Notes |
| :--- | :--- | :--- |
| **QuanTAlib** | ✅ | Internal consistency (Batch vs Streaming). |
| **TA-Lib** | N/A | Not implemented in TA-Lib. |
| **Skender** | N/A | Not implemented in Skender. |
| **Tulip** | N/A | Not implemented in Tulip. |
| **Ooples** | N/A | Not implemented. |
### Common Pitfalls
- **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.