Effects of maximal fluctuation moment $q$ and detrending polynomial orders on the observed multifractal features within MFDFA

TL;DR

This paper investigates how the choice of q moments range and detrending polynomial order in MFDFA affects the measurement of multifractal properties, providing formulas to correct artificial multiscaling in finite signals.

Contribution

It introduces quantitative corrections for the spread of the generalized Hurst exponent considering different q ranges and polynomial orders in MFDFA.

Findings

Formulas for correcting artificial multiscaling in finite signals.

Analysis of the impact of q range on multifractal measurements.

Evaluation of detrending polynomial order effects on MFDFA results.

Abstract

We focus on the importance of $q$ moments range used within multifractal detrended fluctuation analysis (MFDFA) to calculate the generalized Hurst exponent spread and multifractal properties of signals. Different orders of detrending polynomials are also discussed. In particular, we analyze quantitatively the corrections to the spread of generalized Hurst exponent profile $\Delta h$ allowing to extend the previously found by us formulas for large $q$, describing the level of artificial multiscaling in finite signals, to arbitrary narrower range of $q$ moments used in MFDFA technique in distinct applications.