  Recent studies have found that the log-volatility of asset returns exhibit
roughness. This study investigates roughness or the anti-persistence of Bitcoin
volatility. Using the multifractal detrended fluctuation analysis, we obtain
the generalized Hurst exponent of the log-volatility increments and find that
the generalized Hurst exponent is less than $1/2$, which indicates
log-volatility increments that are rough. Furthermore, we find that the
generalized Hurst exponent is not constant. This observation indicates that the
log-volatility has multifractal property. Using shuffled time series of the
log-volatility increments, we infer that the source of multifractality partly
comes from the distributional property.
