  While relevant stylized facts are observed for Bitcoin markets, we find a
distinct property for the scaling behavior of the cumulative return
distribution. For various assets, the tail index $\mu$ of the cumulative return
distribution exhibits $\mu \approx 3$, which is referred to as "the inverse
cubic law." On the other hand, that of the Bitcoin return is claimed to be $\mu
\approx 2$, which is known as "the inverse square law." We investigate the
scaling properties using recent Bitcoin data and find that the tail index
changes to $\mu \approx 3$, which is consistent with the inverse cubic law.
This suggests that some properties of the Bitcoin market could vary over time.
We also investigate the autocorrelation of absolute returns and find that it is
described by a power-law with two scaling exponents. By analyzing the absolute
returns standardized by the realized volatility, we verify that the Bitcoin
return time series is consistent with normal random variables with time-varying
volatility.
