  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.
