Multifractality and sample size influence on Bitcoin volatility patterns

Tetsuya Takaishi

Papers from arXiv.org

Abstract: The finite sample effect on the Hurst exponent (HE) of realized volatility time series is examined using Bitcoin data. This study finds that the HE decreases as the sampling period $\Delta$ increases and a simple finite sample ansatz closely fits the HE data. We obtain values of the HE as $\Delta \rightarrow 0$, which are smaller than 1/2, indicating rough volatility. The relative error is found to be $1\%$ for the widely used five-minute realized volatility. Performing a multifractal analysis, we find the multifractality in the realized volatility time series, smaller than that of the price-return time series.

Date: 2025-11
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