  This letter investigates the dynamic relationship between market efficiency,
liquidity, and multifractality of Bitcoin. We find that before 2013 liquidity
is low and the Hurst exponent is less than 0.5, indicating that the Bitcoin
time series is anti-persistent. After 2013, as liquidity increased, the Hurst
exponent rose to approximately 0.5, improving market efficiency. For several
periods, however, the Hurst exponent was found to be significantly less than
0.5, making the time series anti-persistent during those periods. We also
investigate the multifractal degree of the Bitcoin time series using the
generalized Hurst exponent and find that the multifractal degree is related to
market efficiency in a non-linear manner.
