Multifractal Flexibly Detrended Fluctuation Analysis

TL;DR

This paper introduces a flexible approach to multifractal detrended fluctuation analysis by allowing the polynomial degree for detrending to vary based on a criterion, improving accuracy for artificial and real-world data.

Contribution

It proposes a novel modification to MFDFA where the polynomial degree is not fixed but adaptively selected, enhancing the method's precision.

Findings

Singularity spectra closely match theoretical expectations.

Significant right shift observed in spectra for real-world data.

Improved accuracy over classical MFDFA.

Abstract

Multifractal time series analysis is a approach that shows the possible complexity of the system. Nowadays, one of the most popular and the best methods for determining multifractal characteristics is Multifractal Detrended Fluctuation Analysis (MFDFA). However, it has some drawback. One of its core elements is detrending of the series. In the classical MFDFA a trend is estimated by fitting a polynomial of degree $m$ where $m=const$. We propose that the degree $m$ of a polynomial was not constant ($m\neq const$) and its selection was ruled by an established criterion. Taking into account the above amendment, we examine the multifractal spectra both for artificial and real-world mono- and the multifractal time series. Unlike classical MFDFA method, obtained singularity spectra almost perfectly reflects the theoretical results and for real time series we observe a significant right side shift of the spectrum.