Multifractal Dynamics of Bitcoin and Ethereum: Evidence from Multifractal Detrended Fluctuation Analysis

This study examines the multifractal behaviour of Bitcoin and Ethereum using 68,086 hourly log returns spanning January 2018 to October 2025, via Multifractal Detrended Fluctuation Analysis (MF-DFA). Full-sample estimation confirms significant multifractality in both assets, with block-bootstrap intervals for spectrum width entirely above zero, while the generalized Hurst exponent at q = 2 is indistinguishable from 0.5. A rolling-window design with 161 overlapping windows traces the time variation of spectrum width and asymmetry. Fat-tailed distributions and long-range correlations, the two candidate sources of multifractality, are separated using surrogate and shuffled realizations tested via Monte Carlo p-values under false-discovery-rate control. Fat tails contribute significantly across all windows for both assets and dominate throughout, whereas long-range correlations are significant in fewer windows, mostly for Bitcoin after 2024 and only sporadically for Ethereum. The spectrum is persistently left-skewed, indicating that large fluctuations drive the scaling behaviour. Bai–Perron structural-break analysis, cross-validated against alternative detectors, dates regime shifts, several of which occur around the COVID-19 crash, the Terra/Luna and FTX collapses, and the 2024 spot-ETF approvals. Results are robust to alternative q-ranges, detrending orders, window lengths, and a volatility-adaptive scheme. The findings characterize cryptocurrency markets as complex systems with regime-dependent complexity, pointing to distributional and nonlinear origins of departures from weak-form market efficiency.