MFDCCA: Multifractal Detrended Cross-Correlation Analysis Algorithm Implementation

This program utilizes fractal methodology to study cross-correlation relationships between two non-stationary time series. The implementation involves detrending the integrated time series using polynomial fits across varying time scales, followed by computation of fluctuation functions and scaling exponents. Key algorithmic components include time series partitioning, local trend removal, and q-order statistical moment calculations for multifractal characterization. The methodology enables deeper understanding of variable interdependencies and offers significant value in analysis and prediction applications. The computational framework can be extended to numerous domains including finance, meteorology, and medical research. The program provides enhanced analytical precision through its robust handling of non-stationary data characteristics, contributing to more accurate predictive capabilities and improved problem-solving in practical applications. The core functions implement window-based detrending covariance calculations and multifractal spectrum derivation through Legendre transforms.