Multifractality and sample size influence on Bitcoin volatility patterns

TL;DR

This paper investigates how sample size affects the estimation of the Hurst exponent in Bitcoin volatility data and reveals multifractality in realized volatility, indicating complex market dynamics.

Contribution

It introduces a finite sample ansatz for the Hurst exponent and demonstrates multifractality in Bitcoin volatility, expanding understanding of market complexity.

Findings

Hurst exponent decreases with larger sampling periods

Finite sample ansatz fits Hurst exponent data well

Realized volatility exhibits multifractality, less than that of price returns

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.