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Multifractality and sample size influence on Bitcoin volatility patterns

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  • Takaishi, Tetsuya

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 Δ increases and a simple finite sample ansatz closely fits the HE data. We obtain HE values of Δ→0, which is 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 that multifractality in the realized volatility time series is smaller than that of the price-return time series.

Suggested Citation

  • Takaishi, Tetsuya, 2025. "Multifractality and sample size influence on Bitcoin volatility patterns," Finance Research Letters, Elsevier, vol. 74(C).
    • Handle: RePEc:eee:finlet:v:74:y:2025:i:c:s1544612324017124
    DOI: 10.1016/j.frl.2024.106683
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    1. Tetsuya Takaishi, 2025. "Impact of the COVID-19 pandemic on the financial market efficiency of price returns, absolute returns, and volatility increment: Evidence from stock and cryptocurrency markets," Papers 2504.18960, arXiv.org.

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