MF-toolkit: A High-Performance Python Library for Multifractal Analysis with Automated Crossover Detection, Source Identification and Application to Gravitational Waves Data

TL;DR

MF-toolkit is a high-performance Python library that automates crossover detection, source identification, and validation for multifractal analysis, demonstrated on gravitational wave data.

Contribution

It introduces fully automatic crossover detection, surrogate data generation, and synthetic data tools to improve multifractal analysis accuracy and reproducibility.

Findings

Automated crossover detection algorithms improve reproducibility.

Application to gravitational wave data reveals multifractal properties.

The library enhances robustness and efficiency of multifractal analysis.

Abstract

Multifractal Detrended Fluctuation Analysis (MFDFA) is a powerful and widely used technique for characterizing the scaling properties and long-range correlations of complex time series. However, its application often involves significant practical challenges, such as the subjective identification of scaling regions (crossovers) and the disambiguation of the physical origins of multifractality. We introduce MF-toolkit, a high-performance, parallelized Python library designed to address these challenges. It integrates three key innovations: (1) fully automatic crossover detection algorithms (CDV-A and SPIC), which remove operator bias and enhance reproducibility; (2) a built-in implementation of the Iterative Amplitude Adjusted Fourier Transform (IAAFT) for generating surrogate data, enabling the robust identification of the source of multifractality; and (3) a comprehensive suite for generating synthetic time series for rigorous validation. We demonstrate the rigor and utility of MF-toolkit through its application to characterize the multifractal properties of non-stationary noise in gravitational wave (LIGO) data. The MF-toolkit library offers a robust, efficient, and user-friendly tool for advanced time series analysis, facilitating more rigorous and reproducible research across physics and other data-intensive fields.