Effect of Detrending on Multifractal Characteristics

Abstract

Dierent variants of multifractal detrended uctuation analysis technique are applied in order to investigate various (articial 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 multifractal detrended uctuation analysis 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.