Multifractality and its sources in the digital currency market

TL;DR

The paper investigates the origins of multifractality in digital-asset time series by applying multifractal cross-correlation analysis (MFCCA) and its MFDFA special case to BTC, ETH, DEX, and NFT markets. It systematically disentangles temporal correlations from heavy-tailed fluctuations using a recently proposed ranking-based and q-Gaussian surrogate framework, revealing that long-range correlations are the primary driver of multifractality, while fat tails broaden the spectrum only in the presence of correlations. Across 2018–2024, BTC and ETH exhibit strong multifractal scaling and cross-correlations, with decentralized and NFT markets showing distinct spectral asymmetries reflecting market maturity and liquidity. The results support the use of multifractal analysis for volatility forecasting and risk monitoring in evolving digital markets and provide a robust methodology to separate genuine complexity from distributional artifacts.$

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, may 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, in the present contribution a recently proposed method of disentangling sources of multifractality in time series was applied 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 are 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.

Figures (15)

• Figure S1: Evolution of the cumulative log-returns $\hat{R}(t)$ of the BTC and ETH over the time period from Jan 1, 2018 to Dec 31, 2024.
• Figure S2: Cumulative distribution function for BTC and ETH by year together with Gaussian, power-law (with $\gamma=3$) and stretched exponential distributions (with $\beta=0.4$).
• Figure S3: The Pearson autocorrelation function calculated from the return moduli for BTC and ETH broken by year.
• Figure S4: The Pearson autocorrelation function calculated from the return moduli for BTC and ETH in 2024 with their original PDFs replaced by the $q$-Gaussian distributions with different values of $q$.
• Figure S6: Multifractal spectra for BTC and ETH in 2024 with their original PDFs replaced by the $q$-Gaussian distributions with different values of $q$.