Dissecting Multifractal detrended cross-correlation analysis

ArXiv ID: 2406.19406 “View on arXiv”

Authors: Unknown

Abstract

In this work we address the question of the Multifractal detrended cross-correlation analysis method that has been subject to some controversies since its inception almost two decades ago. To this end we propose several new options to deal with negative cross-covariance among two time series, that may serve to construct a more robust view of the multifractal spectrum among the series. We compare these novel options with the proposals already existing in the literature, and we provide fast code in C, R and Python for both new and the already existing proposals. We test different algorithms on synthetic series with an exact analytical solution, as well as on daily price series of ethanol and sugar in Brazil from 2010 to 2023.

Keywords: Multifractal Detrended Cross-correlation Analysis (MF-DXA), Time Series Analysis, Multifractal Spectrum, Cross-covariance, Ethanol and Sugar Markets, Commodities

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 5.5/10
  • Quadrant: Lab Rats
  • Why: The paper is densely mathematical, featuring extensive LaTeX formulas for multifractal spectrums, Legendre transforms, and derivations of scaling exponents, which warrants a high math score. Empirical rigor is moderate, as it provides C/R/Python code, tests on synthetic data with known analytical solutions, and real-world price data (ethanol/sugar), but lacks the deep, live backtesting environment typical of production-ready strategies.
  flowchart TD
    A["Research Goal<br>Resolve controversies in MF-DXA<br>handling negative cross-covariances"] --> B["Methodology<br>Propose new options for MF-DXA"]
    B --> C["Data Sources"]
    C --> D["Computation<br>Implement fast code in C/R/Python"]
    
    C --> C1["Synthetic Series<br>(Exact analytical solution)"]
    C --> C2["Real Data<br>Ethanol & Sugar prices (2010-2023)"]
    
    D --> E["Analysis<br>Compare new vs existing methods"]
    E --> F["Key Outcomes<br>Robust Multifractal Spectrum<br>Validated algorithms<br>Published code"]
    
    style A fill:#e1f5fe
    style F fill:#e8f5e8