Multifractal Flexibly Detrended Fluctuation Analysis
arXiv:1510.05115 · doi:10.5506/APhysPolB.46.1925
Abstract
Multifractal time series analysis is a 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 some 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 where . We propose that the degree of a polynomial was not constant () 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 classical MFDFA method, obtained singularity spectra almost perfectly reflects the theoretical results and for real time series we observe a significant right side shift of the spectrum.
15 pages, 9 figures. arXiv admin note: text overlap with arXiv:1212.0354 by other authors