# Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series

@article{Kantelhardt2002MultifractalDF, title={Multifractal Detrended Fluctuation Analysis of Nonstationary Time Series}, author={Jan W. Kantelhardt and Stephan A. Zschiegner and Eva Koscielny-Bunde and Armin Bunde and Shlomo Havlin and Harry Eugene Stanley}, journal={Physica A-statistical Mechanics and Its Applications}, year={2002}, volume={316}, pages={87-114} }

## Figures from this paper

## 2,538 Citations

Characteristics analysis of nonstationary signals based on multifractal detrended fluctuation analysis method

- Physics, EngineeringThe 27th Chinese Control and Decision Conference (2015 CCDC)
- 2015

Nonstationary signal generally exhibits multifractal structure, different from a simple monofractal structure that can be depicted by a single scaling exponent, which requires multiple scaling…

Multifractal detrended fluctuation analysis of sunspot time series

- Physics
- 2006

We use multifractal detrended fluctuation analysis (MF-DFA), to study sunspot number fluctuations. The result of the MF-DFA shows that there are three crossover timescales in the fluctuation…

Multifractal Detrended Fluctuation Analysis of Interevent Time Series in a Modified OFC Model

- Physics
- 2013

We use multifractal detrended fluctuation analysis (MF-DFA) method to investigate the multifractal behavior of the interevent time series in a modified Olami—Feder—Christensen (OFC) earthquake model…

MULTIFRACTAL DETRENDED FLUCTUATION ANALYSIS OF ELECTRIC LOAD SERIES

- Physics
- 2015

Multifractal detrended fluctuation analysis (MF-DFA) method is applied to analyze the daily electric load time series. The results of the MF-DFA show that there are three crossover timescales at…

Quantifying two-dimensional nonstationary signal with power-law correlations by detrended fluctuation analysis

- Engineering
- 2015

In this paper, we develop a new method for the multifractal characterization of two-dimensional nonstationary signal, which is based on the detrended fluctuation analysis (DFA). By applying to two…

Multifractal Detrended Fluctuation Analysis combined with Singular Spectrum Analysis

- Engineering
- 2019

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…

Relationships of exponents in multifractal detrended fluctuation analysis and conventional multifractal analysis

- Physics
- 2011

Multifractal detrended fluctuation analysis (MF-DFA) is a relatively new method of multifractal analysis. It is extended from detrended fluctuation analysis (DFA), which was developed for detecting…

Multifractal moving average analysis and test of multifractal model with tuned correlations

- Physics
- 2011

Multiresolution analysis of fluctuations in non-stationary time series through discrete wavelets

- Computer Science
- 2006

Multifractal detrended fluctuation analysis: Practical applications to financial time series

- MathematicsMath. Comput. Simul.
- 2016

## References

SHOWING 1-10 OF 99 REFERENCES

Effect of nonstationarities on detrended fluctuation analysis.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2002

It is found that introducing nonstationarities to stationary correlated signals leads to the appearance of crossovers in the scaling behavior and it is shown how to develop strategies for preprocessing "raw" data prior to analysis, which will minimize the effects of non stationarities on the scaling properties of the data.

Power spectrum and detrended fluctuation analysis: application to daily temperatures

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 2000

FA and DFA are applied to ambient temperature data from the 20th century with the primary goal to resolve the controversy in literature whether the low frequency behavior of the corresponding power spectral densities are better described by a power law or a stretched exponential.

Multifractal random walk.

- Mathematics, PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

To the knowledge, it is the first multifractal process with continuous dilation invariance properties and stationary increments and it is briefly explained how, in the same way, one can build stationary multifractional processes or positive random measures.

Multifractal characterization of stochastic resonance.

- Computer SciencePhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

It is shown that the degree of multifractality defined as a width of singularity spectrum can be successfully used as a measure of complexity both in the case of periodic and aperiodic (stochastic or chaotic) input signals.

Application of the detrended fluctuation analysis (DFA) method for describing cloud breaking

- Environmental Science, Physics
- 1999

Effect of trends on detrended fluctuation analysis.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2001

It is shown how to use DFA appropriately to minimize the effects of trends, how to recognize if a crossover indicates indeed a transition from one type to a different type of underlying correlation, or if the crossover is due to a trend without any transition in the dynamical properties of the noise.

Multifractality in human heartbeat dynamics

- PhysicsNature
- 1999

This work reports oneidence for multifractality in a biological dynamical system, the healthy human heartbeat, and shows that the multifractal character and nonlinear properties of the healthy heart rate are encoded in the Fourier phases.