CFB - Jurik Composite Fractal Behavior

Overview and Purpose

Composite Fractal Behavior (CFB) is a sophisticated trend duration index developed by Jurik Research. It measures the "fractal efficiency" of price movements across multiple time scales to determine the quality and duration of a trend. Unlike traditional trend indicators that look at a single period, CFB analyzes a spectrum of lookback periods to create a composite index.

CFB is designed to answer the question: "How long has the market been trending efficiently?" It is particularly useful for:

Adjusting the period of other indicators (adaptive indicators).
Filtering out choppy markets.
Identifying the breakdown of long-term trends.

Core Concepts

Fractal Efficiency: Measures how "straight" the price movement is. A straight line has high efficiency; a choppy path has low efficiency.
Composite Index: Instead of relying on a single lookback length, CFB evaluates a wide range of lengths (e.g., 4 to 192 bars) and combines them based on their efficiency.
Adaptive: The indicator adapts to the market's current fractal structure, giving more weight to timeframes where trending behavior is evident.
Trend Duration: The output value represents the approximate duration (in bars) of the current trend.

Common Settings and Parameters

Parameter	Default	Function
Lengths	`[2, 4, ..., 192]`	Array of lookback periods to analyze. Default is a dense array from 2 to 192.
Source	Close	Price data used for calculation.

Pro Tip: CFB values typically range from 0 to the maximum lookback length. A rising CFB indicates a strengthening trend (either up or down), while a falling CFB suggests the trend is breaking down or the market is entering a consolidation phase.

Calculation and Mathematical Foundation

The CFB calculation involves several steps for each lookback length L in the provided set:

Calculate Efficiency Ratio: For each length L, calculate the ratio of the net price movement to the total volatility (path length) over that period.
Ratio_L = \frac{|Price_t - Price_{t-L}|}{\sum_{i=0}^{L-1} |Price_{t-i} - Price_{t-i-1}|}
Filter: Only consider lengths where the efficiency ratio exceeds a threshold (typically 0.25). This filters out noise and weak trends.
Weighted Average: Calculate the weighted average of the qualifying lengths, using the efficiency ratio as the weight.
CFB = \frac{\sum (L \cdot Ratio_L)}{\sum Ratio_L}
where the summation is over all L such that Ratio_L > 0.25.
Decay: If no lengths qualify (i.e., the market is very choppy), the CFB value decays towards 1.0.

C# Implementation

The library provides a high-performance implementation that uses RingBuffer for O(1) updates of the volatility sums.

Single CFB (`Cfb`)

using QuanTAlib;

// Initialize with default lengths
var cfb = new Cfb();

// Or specify custom lengths
var cfbCustom = new Cfb(new int[] { 10, 20, 30, 40, 50 });

// Streaming update
TValue result = cfb.Update(new TValue(time, price));
Console.WriteLine($"Current Trend Duration: {result.Value}");

Zero-Allocation Span API

For performance-critical scenarios:

double[] prices = ...;
double[] output = new double[prices.Length];

// Calculate using default lengths
Cfb.Calculate(prices.AsSpan(), output.AsSpan());

Bar Correction (isNew Parameter)

Cfb supports intra-bar updates:

// Real-time: receive initial tick for new bar
cfb.Update(new TValue(time, 100.5), isNew: true);

// Real-time: price updates within same bar
cfb.Update(new TValue(time, 101.0), isNew: false);

Interpretation Details

High Values: Indicate a strong, persistent trend. The value roughly corresponds to the number of bars the trend has been in effect.
Low Values: Indicate a choppy, non-trending market.
Rising CFB: The trend is gaining strength or duration.
Falling CFB: The trend is losing consistency or ending.

CFB is often used as an input to other adaptive indicators (e.g., JMA) to dynamically adjust their smoothing period based on market conditions.

References

Jurik Research: CFB - Composite Fractal Behavior

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