  This study investigates the volatility of daily Bitcoin returns and
multifractal properties of the Bitcoin market by employing the rolling window
method and examines relationships between the volatility asymmetry and market
efficiency. Whilst we find an inverted asymmetry in the volatility of Bitcoin,
its magnitude changes over time, and recently, it has become small. This
asymmetric pattern of volatility also exists in higher frequency returns. Other
measurements, such as kurtosis, skewness, average, serial correlation, and
multifractal degree, also change over time. Thus, we argue that properties of
the Bitcoin market are mostly time dependent. We examine efficiency-related
measures: the Hurst exponent, multifractal degree, and kurtosis. We find that
when these measures represent that the market is more efficient, the volatility
asymmetry weakens. For the recent Bitcoin market, both efficiency-related
measures and the volatility asymmetry prove that the market becomes more
efficient.
