  Multifractal analysis is a forecasting technique used to study the scaling
regularity properties of financial returns, to analyze the long-term memory and
predictability of financial markets. In this paper, we propose a novel
structural detrended multifractal fluctuation analysis (S-MF-DFA) to
investigate the efficiency of the main cryptocurrencies. The new methodology
generalizes the conventional approach by allowing it to proceed on the
different fluctuation regimes previously determined using a change-points
detection test. In this framework, the characterization of the various
exogenous factors influencing the scaling behavior is performed on the basis of
a single-factor model, thus creating a kind of self-explainable machine
learning for price forecasting. The proposal is tested on the daily data of the
three among the main cryptocurrencies in order to examine whether the digital
market has experienced upheavals in recent years and whether this has in some
ways led to a structured multifractal behavior. The sampled period ranges from
April 2017 to December 2022. We especially detect common periods of local
scaling for the three prices with a decreasing multifractality after 2018.
Complementary tests on shuffled and surrogate data prove that the distribution,
linear correlation, and nonlinear structure also explain at some level the
structural multifractality. Finally, prediction experiments based on neural
networks fed with multi-fractionally differentiated data show the interest of
this new self-explained algorithm, thus giving decision-makers and investors
the ability to use it for more accurate and interpretable forecasts.
