Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) Method

The Multifractal Detrended Cross-Correlation Analysis (MF-DCCA) method is a computational technique for quantifying cross-correlations between different time series. This methodology can be implemented through various approaches, including MF-based detrended fluctuation analysis variants like MF-X-DFA. The algorithm typically involves partitioning time series into segments, detrending local trends using polynomial fitting, calculating fluctuation functions for different segment sizes, and analyzing scaling exponents to characterize multifractal properties. This method enables quantitative determination of relationships between non-stationary time series through multifractal spectrum analysis. Key implementation steps include computing q-order fluctuation functions and performing multifractal scaling exponent extraction. The technique finds broad applications across finance, physics, biology, and social sciences for enhanced understanding and prediction of time series correlations, particularly useful for analyzing cross-market dependencies or physiological signal interactions.