标题： 多重分形性和样本大小对比特币波动模式的影响 显示英文标题

标题： Multifractality and sample size influence on Bitcoin volatility patterns

摘要： 研究了比特币数据中实现波动率时间序列的赫斯特指数（HE）的有限样本效应。 本研究发现，随着采样周期$\Delta$的增加，HE 会减小，并且一个简单的有限样本假设能很好地拟合 HE 数据。 我们得到的 HE 值为$\Delta \rightarrow 0$，这些值小于 1/2，表明波动率是粗糙的。 发现广泛使用的五分钟实现波动率的相对误差为$1\%$。 进行多分形分析，我们发现实现波动率时间序列中存在多分形性，其多分形性小于价格收益率时间序列的多分形性。 显示英文摘要

摘要： 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.