Intrinsic multifractality and adaptive efficiency in Bitcoin: Disentangling sources of scaling complexity across market regimes

초록

We characterize the multifractal scaling of Bitcoin returns using approximately 774,000 fiveminute observations spanning August 2017 to December 2024. Three methodological innovations distinguish this study from prior multifractal analyses of cryptocurrency markets. First, we adopt the q-Gaussian rescaling framework recently developed by Kluszczy & nacute;ski et al. (2025) to disentangle genuine from spurious multifractality, replacing the conventional but mathematically problematic decomposition that treats temporal correlations and fat tails as additive sources. Second, we identify and characterize a statistically significant scaling crossover at approximately twenty-five days, separating a near-efficient short-time regime from an anti-persistent long-time regime while singularity spectrum width remains essentially invariant across the two regimes. Third, we contrast pre-and post-ETF market behavior to provide quantitative evidence for adaptive efficiency: the Market Deficiency Measure declines by more than half following the January 2024 spot ETF approval, accompanied by a substantial reduction in long-range dependence. The observed Bitcoin multifractality is genuine in the sense of Kluszczy & nacute;ski et al. (2023): nonlinear temporal correlations are necessary, while fat tails play an amplifying role conditional on those correlations. Across the rolling-window panel of estimates, realized volatility and multifractal complexity are negatively coupled at high statistical significance, consistent with regime-dependent multiplicative cascades in which high-volatility episodes are dominated by a single class of large fluctuations and therefore display narrower singularity spectra. Together, these results offer a coherent multifractal characterization of Bitcoin price formation that aligns with the Adaptive Markets Hypothesis and with the broader statistical-physics framework of price scaling complexity.

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