Multifractal Detrended Fluctuation Analysis combined with Singular Spectrum Analysis

Anton Karmatskii

Ural Federal University, 620026 Yekaterinburg, Russia

Abstract: This paper addresses the problem of finding appropriate method for analysis of non-stationary time series with complex trends and possibly with distinct periodic components in power spectrum. A well established Multifractal Detrended Fluctuation Analysis (MDFA) combined with Singular Spectrum Analysis (SSA) used on several artificial examples to demonstrate the capabilities of the method. In this combined method SSA is used for nonparametric periodic components extraction and for adaptive automatic nonparametric trend extraction. As usual, the local fractal characteristics of the signal are studied by utilizing the MFDFA algorithm. It is shown that combined method is capable of accurately extracting fractal features when signal is contaminated with broadband and narrowband noise. The main task that the author focused on when creating the method was the analysis of currents through ion channels in cell membrane.

Keywords: SSA, DFA, nonparametric.

Pages: 85 – 93 | Full PDF Paper