Complexity of Financial Time Series: Multifractal and Multiscale Entropy Analyses

ArXiv ID: 2507.23414 “View on arXiv”

Authors: Oday Masoudi, Farhad Shahbazi, Mohammad Sharifi

Abstract

We employed Multifractal Detrended Fluctuation Analysis (MF-DFA) and Refined Composite Multiscale Sample Entropy (RCMSE) to investigate the complexity of Bitcoin, GBP/USD, gold, and natural gas price log-return time series. This study provides a comparative analysis of these markets and offers insights into their predictability and associated risks. Each tool presents a unique method to quantify time series complexity. The RCMSE and MF-DFA methods demonstrate a higher complexity for the Bitcoin time series than others. It is discussed that the increased complexity of Bitcoin may be attributable to the presence of higher nonlinear correlations within its log-return time series.

Keywords: Multifractal Detrended Fluctuation Analysis (MF-DFA), Sample Entropy, Time Series Complexity, Log-Returns, Fractal Analysis, Commodities / Cryptocurrencies / Forex

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats
  • Why: The paper is mathematically dense, employing advanced techniques like Multifractal Detrended Fluctuation Analysis (MF-DFA) and Refined Composite Multiscale Sample Entropy (RCMSE) with detailed derivations. However, it lacks backtesting, implementation code, or practical trading metrics, focusing instead on theoretical analysis of time series complexity.
  flowchart TD
    A["Research Goal: <br>Quantify Complexity of Financial Time Series"] --> B["Input Data: <br>Log-Returns of BTC, GBP/USD, Gold, Gas"]
    B --> C["Method 1: MF-DFA <br>Fractal Scaling & Multifractality"]
    B --> D["Method 2: RCMSE <br>Nonlinear Regularity & Predictability"]
    C --> E["Computational Analysis <br>Python (Numpy/PyEntropy)"]
    D --> E
    E --> F{"Key Findings"}
    F --> G["Bitcoin: Highest Complexity <br>Strong Nonlinear Correlations"]
    F --> H["Commodities/Forex: <br>Lower Complexity/Lower Entropy"]