Multifractality and Its Sources in the Digital Currency Market

Stanisław Drożdż (), Robert Kluszczyński, Jarosław Kwapień and Marcin Wątorek
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Stanisław Drożdż: Faculty of Computer Science and Mathematics, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland
Robert Kluszczyński: Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Kraków, Poland
Jarosław Kwapień: Complex Systems Theory Department, Institute of Nuclear Physics, Polish Academy of Sciences, Radzikowskiego 152, 31-342 Kraków, Poland
Marcin Wątorek: Faculty of Computer Science and Mathematics, Cracow University of Technology, ul. Warszawska 24, 31-155 Kraków, Poland

Future Internet, 2025, vol. 17, issue 10, 1-23

Abstract: Multifractality in time series analysis characterizes the presence of multiple scaling exponents, indicating heterogeneous temporal structures and complex dynamical behaviors beyond simple monofractal models. In the context of digital currency markets, multifractal properties arise due to the interplay of long-range temporal correlations and heavy-tailed distributions of returns, reflecting intricate market microstructure and trader interactions. Incorporating multifractal analysis into the modeling of cryptocurrency price dynamics enhances the understanding of market inefficiencies. It may also improve volatility forecasting and facilitate the detection of critical transitions or regime shifts. Based on the multifractal cross-correlation analysis (MFCCA) whose spacial case is the multifractal detrended fluctuation analysis (MFDFA), as the most commonly used practical tools for quantifying multifractality, we applied a recently proposed method of disentangling sources of multifractality in time series to the most representative instruments from the digital market. They include Bitcoin (BTC), Ethereum (ETH), decentralized exchanges (DEX) and non-fungible tokens (NFT). The results indicate the significant role of heavy tails in generating a broad multifractal spectrum. However, they also clearly demonstrate that the primary source of multifractality encompasses the temporal correlations in the series, and without them, multifractality fades out. It appears characteristic that these temporal correlations, to a large extent, do not depend on the thickness of the tails of the fluctuation distribution. These observations, made here in the context of the digital currency market, provide a further strong argument for the validity of the proposed methodology of disentangling sources of multifractality in time series.

Keywords: complexity; time series analysis; nonlinear correlations; multifractality; singularity spectra; q -Gaussian distributions; digital financial instruments (search for similar items in EconPapers)
JEL-codes: O3 (search for similar items in EconPapers)
Date: 2025
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