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

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.