Paper: arXiv 2507.23414

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.

Complexity vs Empirical Score

  • Math Complexity: 9.5/10
  • Empirical Rigor: 3.0/10
  • Quadrant: Lab Rats — theoretically deep, empirically untested

Why this score: 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.

Research Flowchart

  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"]

Cited References (28)

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  6. Wavelet Entropy and Complexity–Entropy Curves Approach for Energy Commodity Price Predictability Amid the Transition to Alternative Energy Sources (2024)
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  8. Multiscale Entropy Analysis of Traffic Time Series (2013)
and 20 more
  1. Multiscale Entropy Analysis of Biological Signals (2005)
  2. Entropy Measures for Biological Signal Analyses (2012)
  3. Multiscale Permutation Entropy of Physiological Time Series (2005)
  4. On Multiscale Entropy Analysis for Physiological Data (2006)
  5. Multiscale Entropy Analysis of Financial Time Series (2012)
  6. Who Dominate the Information Flowing Between Innovative and Traditional Financial Assets? A Multiscale Entropy-Based Approach (2024)
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  10. Multiscale Sample Entropy and Cross-Sample Entropy Based on Symbolic Representation and Similarity of Stock Markets (2018)
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  13. Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series (2002)
  14. Multifractal Analysis of the WTI Crude Oil Market, US Stock Market and EPU (2020)
  15. Inner Multifractal Dynamics in the Jumps of Cryptocurrency and Forex Markets (2024)
  16. The Multiscale Entropy Algorithm and Its Variants: A Review (2015)
  17. Analysis of Complex Time Series Using Refined Composite Multiscale Entropy (2014)
  18. Adaptive Computation of Multiscale Entropy and Its Application in EEG Signals for Monitoring Depth of Anesthesia During Surgery (2012)
  19. Multifractality and Non-Gaussianity of Eye Fixation Duration Time Series in Reading Persian Texts (2019)
  20. Tests for Skewness, Kurtosis, and Normality for Time Series Data (2005)

0 of 28 cited works are in the corpus; resolved via arXiv source bundles, Semantic Scholar and OpenAlex. Corpus-wide: 2518 linked papers.