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 investigatedand 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 thatfor the fat-tailed distribution .
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 .
D
high frequency
A
,
R
with large time scales
for large sampling periods
R
short time scales
time scales shorter than one day
R
large time scales
time scales longer than about one week
A
,
R
volatility asymmetry
it
R
also investigatedand it is confirmed
investigated, confirming
R
the multifractality, and the degree of multifractality for the temporal correlation is stronger than thatfor the fat-tailed distribution
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