  The bitcoin price has surged in recent years and it has also exhibited phases
of rapid decay. In this paper we address the question to what extent this novel
cryptocurrency market can be viewed as a classic or semi-efficient market.
Novel and robust tools for estimation of multi-fractal properties are used to
show that the bitcoin price exhibits a very interesting multi-scale correlation
structure. This structure can be described by a power-law behavior of the
variances of the returns as functions of time increments and it can be
characterized by two parameters, the volatility and the Hurst exponent. These
power-law parameters, however, vary in time. A new notion of generalized Hurst
exponent is introduced which allows us to check if the multi-fractal character
of the underlying signal is well captured. It is moreover shown how the
monitoring of the power-law parameters can be used to identify regime shifts
for the bitcoin price. A novel technique for identifying the regimes switches
based on a goodness of fit of the local power-law parameters is presented. It
automatically detects dates associated with some known events in the bitcoin
market place. A very surprising result is moreover that, despite the wild ride
of the bitcoin price in recent years and its multi-fractal and non-stationary
character, this price has both local power-law behaviors and a very orderly
correlation structure when it is observed on its entire period of existence.
