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

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.