MULTIFRACTAL FLEXIBLY DETRENDED FLUCTUATION ANALYSIS

Multifractal time series analysis is an 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 a 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 not equal 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 the classical MFDFA method, obtained singularity spectra almost perfectly reflect the theoretical results, and for real time series, we observe a significant shift at the right-hand side of the spectrum.