Multifractal Characteristics of One-Dimensional Time Series

Resource Overview

This function computes the multifractal characteristics of a one-dimensional time series, implementing algorithms for fractal dimension analysis across multiple scales.

Detailed Documentation

This function analyzes the multifractal characteristics of a one-dimensional time series. Multifractal analysis is a method for characterizing self-similarity in time series by decomposing the series into local regions at different scales and calculating the fractal dimension for each local region at every scale. The implementation typically involves techniques such as wavelet transform modulus maxima (WTMM) or multifractal detrended fluctuation analysis (MF-DFA) to compute singularity spectra and generalized fractal dimensions. This function can be used to study the complexity and self-similarity properties of time series, thereby extracting characteristic patterns and underlying regularities. Key computational steps may include signal preprocessing, scale selection, fluctuation function calculation, and Legendre transformation for spectrum derivation.