Paper: arXiv 2406.19406

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.

Complexity vs Empirical Score

  • Math Complexity: 7.5/10
  • Empirical Rigor: 5.5/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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

Cited References (18)

  1. On the fractal properties of cosmic rays and Sun dynamics cross-correlations (2022) — link
  2. Multifractal Cross-Correlations of Bitcoin and Ether Trading Characteristics in the Post-COVID-19 Time (2022) — link
  3. Multifractal characterization and cross correlations of reference evapotranspiration time series of India (2021) — link
  4. Multifractal detrended cross-correlation analysis on benchmark cryptocurrencies and crude oil prices (2020) — link
  5. Multifractal detrended cross-correlation analysis of wind speed and solar radiation. (2020) — link
  6. MULTIFRACTAL ANALYSIS OF BRAZILIAN AGRICULTURAL MARKET (2020) — link
  7. Multifractal detrended cross-correlation analysis between respiratory diseases and haze in South Korea (2020) — link
  8. Multifractal Detrended Cross-Correlation Analysis of Global Methane and Temperature (2020) — link
and 10 more
  1. Detecting correlations and triangular arbitrage opportunities in the Forex by means of multifractal detrended cross-correlations analysis (2019) — link
  2. Fractals (2018) — link
  3. Cross-correlations between the US monetary policy, US dollar index and crude oil market (2017) — link
  4. Detrended cross-correlations between returns, volatility, trading activity, and volume traded for the stock market companies (2015) — link
  5. The Economics of Brazil’s Ethanol-Sugar Markets, Mandates, and Tax Exemptions (2015) — link
  6. Detecting and interpreting distortions in hierarchical organization of complex time series. (2015) — link
  7. Detrended cross-correlation analysis consistently extended to multifractality. (2013) — link
  8. Multifractal detrended cross-correlation analysis for two nonstationary signals. (2008) — link
  9. Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series (2002) — link
  10. Plenum press, New York, NY, USA (1988)

0 of 18 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.