Effect of detrending on multifractal characteristics

TL;DR

This paper investigates how the choice of detrending polynomial order in multifractal detrended fluctuation analysis (MFDFA) affects the characterization of time series, revealing sensitivity and signal-dependent relations.

Contribution

It demonstrates the impact of polynomial order on multifractal spectrum width and Hurst exponent, providing insights into the correlation structure of different signals.

Findings

Singularity spectra are highly sensitive to detrending polynomial order.

The relation between spectrum width and polynomial order varies with signal type.

Analysis can reveal additional information about the correlation structure of time series.

Abstract

Different variants of MFDFA technique are applied in order to investigate various (artificial and real-world) time series. Our analysis shows that the calculated singularity spectra are very sensitive to the order of the detrending polynomial used within the MFDFA method. The relation between the width of the multifractal spectrum (as well as the Hurst exponent) and the order of the polynomial used in calculation is evident. Furthermore, type of this relation itself depends on the kind of analyzed signal. Therefore, such an analysis can give us some extra information about the correlative structure of the time series being studied.