Understanding emerging properties through multi-scaling nature in the financial market

초록

Multifractality in financial time series has been extensively reported as a potential signature of complex market dynamics, with implications for risk management, market efficiency, and extreme event prediction. Empirical studies suggest that asset returns and volatility exhibit multiscale behavior across time horizons. However, the existence and interpretation of multifractality remain controversial. While it is often attributed to nonlinear correlations and long-range memory, evidence shows that multifractal features may persist after random shuffling, highlighting the role of heavy-tailed return distributions. In addition, multifractal analysis is highly sensitive to methodological choices, and the limited length of financial time series raises concerns about statistical reliability and finite-scale effects. This mini review critically examines multifractality in financial markets by summarizing both supporting evidence and major criticisms. We review commonly used analytical approaches, including multifractal detrended fluctuation analysis, fluctuation-based methods, and partition function techniques, emphasizing their limitations and potential biases. Recent empirical studies questioning the universality of multifractality are discussed, with particular attention to market microstructure and aggregation effects. Finally, we outline open issues and future research directions, stressing the need for robust statistical validation, surrogate data analysis, and stronger links between empirical findings and microstructural or agent-based modeling frameworks.

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