Multifractal Detrended Fluctuation Analysis Computation

Multifractal Detrended Fluctuation Analysis (MFDFA) represents a sophisticated mathematical approach for characterizing complex time series data. The MATLAB implementation typically involves several key computational stages: data preprocessing, trend removal through polynomial fitting, fluctuation function calculation across multiple scales, and multifractal spectrum estimation. Core algorithm components include: - Wavelet transform implementations for multi-scale decomposition - Hurst exponent calculation using segmented regression - q-order statistical moment analysis for multifractal characterization - Detrending procedures using adaptive window sizes The MATLAB code structure generally comprises: 1. Main function handling data input and parameter initialization 2. Subfunctions for local trend estimation (often using linear or quadratic fitting) 3. Fluctuation computation modules with scale-dependent processing 4. Multifractal spectrum generation through Legendre transformation This methodology finds critical applications across diverse domains including financial market analysis, meteorological pattern recognition, and physiological signal processing. Continuous refinement of MATLAB implementations focuses on computational efficiency improvements through vectorization, parallel processing capabilities, and optimized memory management for large-scale datasets.