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Multifractal analysis is a forecasting technique used to study the scalingregularity properties of financial returns, to analyze the long-term memory andpredictability of financial markets. In this paper, we propose a novelstructural detrended multifractal fluctuation analysis (S-MF-DFA) toinvestigate the efficiency of the main cryptocurrencies. The new methodologygeneralizes the conventional approach by allowing it to proceed on thedifferent fluctuation regimes previously determined using a change-pointsdetection test. In this framework, the characterization of the variousexogenous factors influencing the scaling behavior is performed on the basis ofa single-factor model, thus creating a kind of self-explainable machinelearning for price forecasting. The proposal is tested on the daily data of thethree among the main cryptocurrencies in order to examine whether the digitalmarket has experienced upheavals in recent years and whether this has in someways led to a structured multifractal behavior. The sampled period ranges fromApril 2017 to December 2022. We especially detect common periods of localscaling 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 thestructural multifractality. Finally, prediction experiments based on neuralnetworks fed with multi-fractionally differentiated data show the interest ofthis new self-explained algorithm, thus giving decision-makers and investorsthe ability to use it for more accurate and interpretable forecasts.

Structured Multifractal Scaling of the Principal Cryptocurrencies: Examination using a Self-Explainable Machine Learning