Using 1-min high frequency 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 with large time scales, kurtosis is anticipated to approach the Gaussian expectation, we find that convergence to that is very slow. Skewness is found to be negative at small time scales and becomes consistent with zero at large time scales. We also investigate daily volatility-asymmetry by using GARCH, GJR, and RGARCH models and find no evidence of volatility asymmetry. On exploring multifractality using multifractal detrended fluctuation analysis, we find that the Bitcoin time series exhibits multifractality. The sources of multifractality are also investigated and it is confirmed that both temporal correlation and the fat-tailed distribution contribute to the multifractality, and the degree of multifractality for the time correlation is stronger than that for the fat-tailed distribution.
Using 1-min high frequency 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 with large time scales, kurtosis is anticipated to approach the Gaussian expectation, we find that convergence to that is very slow. Skewness is found to be negative at short time scales and becomes consistent with zero at large time scales. We also investigate daily volatility-asymmetry by using GARCH, GJR, and RGARCH models and find no evidence of volatility asymmetry. On exploring multifractality using multifractal detrended fluctuation analysis, we find that the Bitcoin time series exhibits multifractality. The sources of multifractality are also investigated and it is confirmed that both temporal correlation and the fat-tailed distribution contribute to the multifractality, and the degree of multifractality for the temporal correlation is stronger than that for the fat-tailed distribution.
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