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Bitcoin Realized Volatility: Sampling Effects and Multifractality

Article arXiv papers · Author: Tetsuya Takaishi
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Summary

The study examines how finite sample size affects estimates of the Hurst exponent for Bitcoin realized volatility. It finds that the estimated exponent falls as the sampling interval grows and that a simple finite-sample relationship fits the observations. Extrapolating toward very fine sampling yields values below one-half, which the authors interpret as evidence of rough volatility. At the commonly used five-minute interval, the reported relative error is one percent.

The paper also applies multifractal analysis to realized volatility and compares its multifractality with that of Bitcoin returns. Volatility is found to be less multifractal than returns. These findings concern statistical properties of the sampled series; the supplied description does not specify the data span, estimator details, robustness checks, or trading applications, so the results should not be read as a direct forecasting or strategy result.

Key ideas

  • The estimated Hurst exponent for realized volatility decreases as the sampling interval increases.
  • A simple finite-sample ansatz closely fits the observed exponent estimates.
  • Extrapolated Hurst exponent values below one-half indicate rough Bitcoin volatility.
  • At five-minute sampling, the reported relative error is one percent.
  • Bitcoin realized volatility exhibits less multifractality than price returns.

Tags

CryptoVolatilityStatistics
Full text
# Multifractality and sample size influence on Bitcoin volatility patterns


# 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 $Δ$ increases and a simple finite sample ansatz closely fits the HE data. We obtain values of the HE as $Δ\rightarrow 0$, 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.

Shown in full with attribution under the source's licence. Licence: abstract CC0

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.