Structured multifractal scaling of the principal cryptocurrencies: Examination using a self‐explainable machine learning

Abstract

This paper introduces a novel statistical testing technique known as segmented detrended multifractal fluctuation analysis (SMF‐DFA) to analyze the structured scaling properties of financial returns and predict the long‐term memory of financial markets. The proposed methodology is applied to assess the efficiency of major cryptocurrencies, expanding upon conventional approaches by incorporating different fluctuation regimes identified through a change‐point detection test. A single‐factor model is employed to characterize the endogenous factors influencing scaling behavior, leading to the development of a self‐explanatory machine learning approach for price forecasting. The proposed method is evaluated using daily data from three major cryptocurrencies spanning from April 2017 to December 2022. The analysis aims to determine whether the digital market has experienced significant changes in recent years and assess whether this has resulted in structured multifractal behavior. The study identifies common periods of local scaling among the three prices, with a noticeable decrease in multifractality observed after 2018. Furthermore, complementary tests on shuffled and surrogate data are conducted to explore the distribution, linear correlation, and nonlinear structure, shedding light on the explanation of structured multifractality to some extent. Additionally, prediction experiments based on neural networks fed with multi‐fractionally differentiated data demonstrate the utility of this new self‐explanatory algorithm for decision‐makers and investors seeking more accurate and interpretable forecasts.