Multifractality and sample size influence on Bitcoin volatility patterns

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 $\mathrm{\Delta }$ increases and a simple finite sample ansatz closely fits the HE data. We obtain values of the HE as $\mathrm{\Delta }\to 0$, which are smaller than 1/2, indicating rough volatility. The relative error is found to be $1\mathrm{\%}$ 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.