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We perform a comparative study of applicability of the Multifractal Detrended Fluctuation Analysis (MFDFA) and the Wavelet Transform Modulus Maxima (WTMM) method in proper detecting of mono- and multifractal character of data. We quantify…
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…
We develop a method for the multifractal characterization of nonstationary time series, which is based on a generalization of the detrended fluctuation analysis (DFA). We relate our multifractal DFA method to the standard partition…
Multifractal analysis has become a powerful signal processing tool that characterizes signals or images via the fluctuations of their pointwise regularity, quantified theoretically by the so-called multifractal spectrum. The practical…
We illustrate the efficacy of a discrete wavelet based approach to characterize fluctuations in non-stationary time series. The present approach complements the multi-fractal detrended fluctuation analysis (MF-DFA) method and is quite…
Multifractal analysis studies signals, functions, images or fields via the fluctuations of their local regularity along time or space, which capture crucial features of their temporal/spatial dynamics. It has become a standard signal and…
A recently developed wavelet based approach is employed to characterize the scaling behavior of spectral fluctuations of random matrix ensembles, as well as complex atomic systems. Our study clearly reveals anti-persistent behavior and…
We review the central results concerning wavelet methods in multifractal analysis, which consists in analysis of the pointwise singularities of a signal, and we describe its recent extension to multivariate multifractal analysis, which…
We study the multifractal temporal scaling properties of river discharge and precipitation records. We compare the results for the multifractal detrended fluctuation analysis method with the results for the wavelet transform modulus maxima…
In a recent work Manimaran et al. [Manimaran et al., Phys. Rev. E 72, 046120 (2005)] propose to use multiresolution Daubechies (DB) wavelets to (detrend) remove the low frequency trends and subsequently to quantify the multifractal…
The wavelet transform and related techniques are used to analyze singular and fractal signals. The normalized wavelet scalogram is introduced to detect singularities including jumps, cusps and other sharply changing points. The wavelet…
Recently the statistical characterizations of financial markets based on physics concepts and methods attract considerable attentions. We used two possible procedures of analyzing multifractal properties of a time series. The first one uses…
Based on the Multifractal Detrended Fluctuation Analysis (MFDFA) and on the Wavelet Transform Modulus Maxima (WTMM) methods we investigate the origin of multifractality in the time series. Series fluctuating according to a qGaussian…
We propose a wavelet based method for the characterization of the scaling behavior of non-stationary time series. It makes use of the built-in ability of the wavelets for capturing the trends in a data set, in variable window sizes.…
Periodically driven, or Floquet, disordered quantum systems have generated many unexpected discoveries of late, such as the anomalous Floquet Anderson insulator and the discrete time crystal. Here, we report the emergence of an entire band…
In this study, we challenge the traditional approach of frequency analysis on directed graphs, which typically relies on a single measure of signal variation such as total variation. We argue that the inherent directionality in directed…
We study quantitatively the level of false multifractal signal one may encounter while analyzing multifractal phenomena in time series within multifractal detrended fluctuation analysis (MF-DFA). The investigated effect appears as a result…
We present two methods for detecting patterns and clusters in high dimensional time-dependent functional data. Our methods are based on wavelet-based similarity measures, since wavelets are well suited for identifying highly discriminant…
The refractive index fluctuations in the connective tissue layer (stroma) of human cervical tissues having different grades of precancers (dysplasia) was quantified using a wavelet-based multifractal detrended fluctuation analysis model.…
This contribution addresses the question commonly asked in scientific literature about the sources of multifractality in time series. Two primary sources are typically considered. These are temporal correlations and heavy tails in the…