Bitcoin Returns, Volatility Asymmetry, and Multifractality Across Time Scales

Summary

This study analyzes one-minute Bitcoin returns to describe their distribution, behavior across sampling intervals, volatility asymmetry, and multifractal properties. It reports fat tails and kurtosis far from the Gaussian benchmark, with kurtosis approaching that benchmark only slowly as the sampling period grows. Return skewness is negative at intervals shorter than a day and becomes consistent with zero at intervals longer than about a week.

For daily volatility asymmetry, the authors apply GARCH, GJR, and RGARCH models and find no evidence of an effect. They use multifractal detrended fluctuation analysis to identify multifractality, then examine its sources and conclude that both temporal correlation and heavy tails contribute. The study also compares the multifractal properties of Bitcoin and GBP–USD around the Brexit vote: the exchange rate was affected, while Bitcoin was reported as robust. These are statistical findings for the examined series and event; they do not establish a trading strategy or show that the observed patterns will persist.

Key ideas

• One-minute Bitcoin returns have fat tails and kurtosis that converges slowly toward the Gaussian benchmark at longer sampling intervals.
• Bitcoin return skewness is negative at short time scales and consistent with zero at much longer scales.
• GARCH-family models provide no evidence of daily volatility asymmetry in the analyzed Bitcoin data.
• Multifractal detrended fluctuation analysis identifies multifractality associated with both temporal correlation and fat-tailed returns.
• Around Brexit, GBP–USD showed a multifractal response while Bitcoin was reported as robust.

Tags

# Statistical properties and multifractality of Bitcoin


# Statistical properties and multifractality of Bitcoin









Using 1-min returns of Bitcoin prices, we investigate statistical properties and multifractality of a Bitcoin time series. We find that the 1-min return distribution is fat-tailed, and kurtosis largely deviates from the Gaussian expectation. Although for large sampling periods, kurtosis is anticipated to approach the Gaussian expectation, we find that convergence to that is very slow. Skewness is found to be negative at time scales shorter than one day and becomes consistent with zero at time scales longer than about one week. We also investigate daily volatility-asymmetry by using GARCH, GJR, and RGARCH models, and find no evidence of it. On exploring multifractality using multifractal detrended fluctuation analysis, we find that the Bitcoin time series exhibits multifractality. The sources of multifractality are investigated, confirming that both temporal correlation and the fat-tailed distribution contribute to it. The influence of "Brexit" on June 23, 2016 to GBP--USD exchange rate and Bitcoin is examined in multifractal properties. We find that, while Brexit influenced the GBP--USD exchange rate, Bitcoin was robust to Brexit.

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.