Detecting Long-range Correlations with Detrended Fluctuation Analysis

Abstract

We examine the Detrended Fluctuation Analysis (DFA), which is a well-established method for the detection of long-range correlations in time series. We show that deviations from scaling that appear at small time scales become stronger in higher orders of DFA, and suggest a modified DFA method to remove them. The improvement is necessary especially for short records that are affected by non-stationarities. Furthermore, we describe how crossovers in the correlation behavior can be detected reliably and determined quantitatively and show how several types of trends in the data affect the different orders of DFA.

10 pages, including 8 figures

Cited by in corpus (196)

• Multifractal detrended fluctuation analysis of nonstationary time series
• Effect of Trends on Detrended Fluctuation Analysis
• Effect of nonstationarities on detrended fluctuation analysis
• Multifractal detrended cross-correlation analysis for two nonstationary signals
• Stochastic models which separate fractal dimension and Hurst effect
• Multifractal analysis of financial markets
• Multifractal detrending moving average cross-correlation analysis
• Multifractal Properties of Price Fluctuations of Stocks and Commodities
• Multifractal Detrended Fluctuation Analysis of Sunspot Time Series
• Comparison of detrending methods for fluctuation analysis
• Effect of nonlinear filters on detrended fluctuation analysis
• Detrended fluctuation analysis for fractals and multifractals in higher dimensions
• Multiscale characteristics of the emerging global cryptocurrency market
• Power-law persistence and trends in the atmosphere: A detailed study of long temperature records
• Switchbacks in the near-Sun magnetic field: long memory and impact on the turbulence cascade
• Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces
• Characterization of Sleep Stages by Correlations of Heartbeat Increments
• Comparing the performance of FA, DFA and DMA using different synthetic long-range correlated time series
• Statistical physics approaches to the complex Earth system
• Fractal Analysis of River Flow Fluctuations (with Erratum)
• Multifractal Detrended Cross-Correlation Analysis of Sunspot Numbers and River Flow Fluctuations
• Long term persistence in the sea surface temperature fluctuations
• Bursty Human Dynamics
• Global climate models violate scaling of the observed atmospheric variability
• Effect of extreme data loss on long-range correlated and anti-correlated signals quantified by detrended fluctuation analysis
• Fractal scale-invariant and nonlinear properties of cardiac dynamics remain stable with advanced age: A new mechanistic picture of cardiac control in healthy elderly
• Degree distribution of the visibility graphs mapped from fractional Brownian motions and multifractal random walks
• A Multifractal Description of Wind Speed Records
• Modified detrended fluctuation analysis based on empirical mode decomposition
• Emergence of long memory in stock volatility from a modified Mike-Farmer model
• Interpretation of heart rate variability via detrended fluctuation analysis and alpha-beta filter
• Multifractal cross-correlations between the World Oil and other Financial Markets in 2012-2017
• Detrended fluctuation analysis as a regression framework: Estimating dependence at different scales
• Communication activity in a social network: relation between long-term correlations and inter-event clustering
• Detrended fluctuation analysis of daily temperature records: Geographic dependence over Australia
• Nonlinear dynamics of human locomotion: effects of rhythmic auditory cueing on local dynamic stability
• Joint multifractal analysis based on the partition function approach: Analytical analysis, numerical simulation and empirical application
• Multifractal Fluctuations in Seismic Interspike Series
• Effect of detrending on multifractal characteristics
• Variance fluctuations in nonstationary time series: a comparative study of music genres
• Persistence in Complex Systems
• Establishing a direct connection between detrended fluctuation analysis and Fourier analysis
• Long-range correlation and multifractality in Bach's Inventions pitches
• Long-memory effects in linear-response models of Earth's temperature and implications for future global warming
• Influence of autocorrelation on the topology of the climate network
• Theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average
• Power-Law Persistence in the Atmosphere: Analysis and Applications
• A phase-resolved XMM-Newton Campaign on the Colliding Wind Binary HD 152248
• Nonlinear analysis of time series of vibration data from a friction brake: SSA, PCA, and MFDFA
• Detrended fluctuation analysis of intertrade durations
• Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant
• p-exponent and p-leaders, Part II: Multifractal Analysis. Relations to Detrended Fluctuation Analysis
• On the multifractal effects generated by monofractal signals
• Testing reanalysis datasets in Antarctica: Trends, persistence properties and trend significance
• Statistical analysis of the overnight and daytime return
• Correlation studies of open and closed states fluctuations in an ion channel: Analysis of ion current through a large conductance locust potassium channel
• Consistency of detrended fluctuation analysis
• Permutation Jensen-Shannon distance: A versatile and fast symbolic tool for complex time series analysis
• Multifractality and long memory of a financial index
• Multifractal and Network Analysis of Phase Transition
• On the scaling ranges of detrended fluctuation analysis for long-memory correlated short series of data
• Effects of long memory in the order submission process on the properties of recurrence intervals of large price fluctuations
• Detrending Moving Average Algorithm: Frequency Response and Scaling Performances
• Recurrence interval analysis of high-frequency financial returns and its application to risk estimation
• Scaling of Horizontal and Vertical Fixational Eye Movements
• Complex systems approach to natural language
• Empirical shape function of limit-order books in the Chinese stock market
• Effects of coarse-graining on the scaling behavior of long-range correlated and anti-correlated signals
• Transient superdiffusion and long-range correlations in the motility patterns of trypanosomatid flagellate protozoa
• Language Time Series Analysis
• Volcanic forcing improves Atmosphere-Ocean Coupled General Circulation Model scaling performance
• Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise
• Visibility graph analysis of economy policy uncertainty indices
• Financial factor influence on scaling and memory of trading volume in stock market
• Statistical properties of volatility return intervals of Chinese stocks
• Anomalous Diffusion and Long-range Correlations in the Score Evolution of the Game of Cricket
• Effects of polynomial trends on detrending moving average analysis
• Multiscale Solar Wind Turbulence Properties inside and near Switchbacks measured by Parker Solar Probe
• Assessment of 48 Stock markets using adaptive multifractal approach
• Early warning signals for critical transitions in complex systems
• Multifractality due to long-range correlation in the L-band ionospheric scintillation S4 index time series
• Long range correlation in cosmic microwave background radiation
• Level Crossing Analysis of the Stock Markets
• The significance of trends in long-term correlated records
• Recurrence interval analysis of trading volumes
• Minimizing the effect of sinusoidal trends in detrended fluctuation analysis
• Scaling and memory in the return intervals of realized volatility
• Detrended fluctuation analysis as a statistical tool to monitor the climate
• Superfamily classification of nonstationary time series based on DFA scaling exponents
• Task-dependent fractal patterns of information processing in working memory
• Turbulence-induced persistence in laser beam wandering
• Computational experiments successfully predict the emergence of autocorrelations in ultra-high-frequency stock returns
• Statistical properties of daily ensemble variables in the Chinese stock markets
• Volatility in atmospheric temperature variability
• Fractal Time Series Analysis of Social Network Activities
• Assessment of long-range correlation in animal behaviour time series: the temporal pattern of locomotor activity of Japanese quail (Coturnix coturnix) and mosquito larva (Culex quinquefasciatus)
• Move-by-move dynamics of the advantage in chess matches reveals population-level learning of the game
• Effects of scarring on quantum chaos in disordered quantum wells
• Quantifying long-range correlations in complex networks beyond nearest neighbors
• Fractal Dynamics in Chaotic Quantum Transport
• Transitions between superstatistical regimes: validity, breakdown and applications
• Long-term correlations and multifractal analysis of trading volumes for Chinese stocks
• Time-varying return predictability in the Chinese stock market
• Multifractality Signatures in Quasars Time Series. I. 3C 273
• Correlated power time series of individual wind turbines: A data driven model approach
• Detrended Fluctuation Analysis of Systolic Blood Pressure Control Loop
• Effects of shady environments on fish collective behavior
• Dynamical Heart Beat Correlations during Running
• Empirical regularities of opening call auction in Chinese stock market
• Detecting and modelling delayed density-dependence in abundance time series of a small mammal (Didelphis aurita)
• Analyzing long-term correlated stochastic processes by means of recurrence networks: Potentials and pitfalls
• Memory and long-range correlations in chess games
• Communication activity in social networks: growth and correlations
• Experimental confirmation of long-memory correlations in star-wander data
• Modeling correlated bursts by the bursty-get-burstier mechanism
• Detecting spatial homogeneity in the world trade web with Detrended Fluctuation Analysis
• On the behavior of the DFA and DCCA in trend-stationary processes
• Investigation on gait by means of factorial moments
• Long-term power-law fluctuation in Internet traffic
• Multifractal Analysis of Pulsar Timing Residuals: Assessment of Gravitational Wave Detection
• Mona Lisa, the stochastic view and fractality in color space
• Blocks adjustment -- reduction of bias and variance of detrended fluctuation analysis using Monte Carlo simulation
• Probabilistic properties of detrended fluctuation analysis for Gaussian processes
• Linear and nonlinear correlations in order aggressiveness of Chinese stocks
• Universal patterns in sound amplitudes of songs and music genres
• Nonlinear stratospheric variability: multifractal detrended fluctuation analysis and singularity spectra
• Multifractal cross-correlation effects in two-variable time series of complex network vertex observables
• Statistical properties of online avatar numbers in a massive multiplayer online role-playing game
• Burst-tree decomposition of time series reveals the structure of temporal correlations
• Changes in long-term properties of the Danube river level and flow induced by damming
• Scaling Features of Price-Volume Cross-Correlation
• Scaling and memory in the non-poisson process of limit order cancelation
• Persistent Homology of Fractional Gaussian Noise
• Pion Fluctuation in High Energy Collisions - A Chaos-based Quantitative Estimation with Visibility Graph Technique
• Fluctuation analysis of high frequency electric power load in the Czech Republic
• Analytically solvable autocorrelation function for weakly correlated interevent times
• Early warnings of tipping in a non-autonomous turbulent reactive flow system: efficacy, reliability, and warning times
• Serial Correlation, Periodicity and Scaling of Eigenmodes in an Emerging Market
• Multivariate Signal Denoising Based on Generic Multivariate Detrended Fluctuation Analysis
• Quantification of scaling exponent with crossover type phenomena for different types of forcing in DC glow discharge plasma
• Multiscale permutation entropy analysis of laser beam wandering in isotropic turbulence
• Exploring the Interplay of Intrinsic Fluctuation and Complexity in Intracellular Calcium Dynamics
• Study of Di-muon Production Process in $pp$ Collision in CMS Data from Symmetry Scaling Perspective
• Scaling and wavelet-based analyses of the long-term heart rate variability of the Eastern Oyster
• Surrogate testing of volatility series from long-range correlated noise
• Statistics of punctuation in experimental literature -- the remarkable case of "Finnegans Wake" by James Joyce
• Asymmetric Roughness of Elastic Interfaces at the Depinning Threshold
• Long-range Correlation and Market Segmentation in Bond Market
• LSTM knowledge transfer for HRV-based sleep staging
• Space, time and velocity association of successive coronal mass ejections
• Markov Properties of Electrical Discharge Current Fluctuations in Plasma
• Identification of Defective Two Dimensional Semiconductors by Multifractal Analysis: The Single-layer $\mathrm{Mo}{\mathrm{S}}_2$ Case Study
• Spectral fluctuation analysis of ionospheric inhomogeneities over Brazilian territory Part II: E-F valley region plasma instabilities
• Dual-induced multifractality in online viewing activity
• The soundscape dynamics of human agglomeration
• A novel entropy recurrence quantification analysis
• Using Space-Filling Curves and Fractals to Reveal Spatial and Temporal Patterns in Neuroimaging Data
• Illusion of persistence in NBA 1995-2018 regular season data
• Pion Fluctuation Study in Pb-Pb Collision at 2.76 TeV per nucleon pair from ALICE Experiment with Chaos and Complex Network-based Methods
• Corrupted bifractal features in finite uncorrelated power-law distributed data
• Temporal scaling theory for bursty time series with clusters of arbitrarily many events
• Burst-tree structure and higher-order temporal correlations
• Evacuation in the Social Force Model is not stationary
• Situations in traffic - how quickly they change
• Scaling analysis of time series of daily prices from stock markets of transitional economies in the Western Balkans
• On the dynamics of bubbles in boiling water
• Long-term persistence and multifractality of river runoff records: Detrended fluctuation studies
• Antipersistent behavior of defects in a lyotropic liquid crystal during annihilation
• Acoustical classification of different speech acts using nonlinear methods
• Neural (EEG) Response during Creation and Appreciation: A Novel Study with Hindustani Raga Music
• Analysis of the autocorrelation function for time series with higher-order temporal correlations: An exponential case
• Deep Particulate Matter Forecasting Model Using Correntropy-Induced Loss
• Persistence of temperature and precipitation: from local to global anomalies
• Appropriateness of correlated first order auto-regressive processes for modeling daily temperature records
• Qualitative Assessment of Gene Expression in Affymetrix Genechip Arrays
• Gestalt Phenomenon in Music? A Neurocognitive Physics Study with EEG
• Heavy-Tailed Features and Empirical Analysis of the Limit Order Book Volume Profiles in Futures Markets
• Microstructure identification via detrended fluctuation analysis of ultrasound signals
• Azimuthal Anisotropy in High Energy Nuclear Collision - An Approach based on Complex Network Analysis
• Multifractal Signatures of Hamiltonian Chaos in Hyperion's Rotational Dynamics
• Is non-Gaussianity sufficient to produce long-range volatile correlations?
• Detrended fluctuation analysis on the correlations of complex networks under attack and repair strategy
• The fractal dimension of music: Melodic contours and time series of pitch
• Characterizing price index behavior through fluctuation dynamics
• MF-toolkit: A High-Performance Python Library for Multifractal Analysis with Automated Crossover Detection, Source Identification and Application to Gravitational Waves Data
• Ordinal language of antipersistent binary walks
• Interplay of transitions between oscillations with emergence of fireballs and quantification of phase coherence, scaling index in a magnetized glow discharge plasma of toroidal assembly
• Stationarity of the detrended price return in stock markets
• Large-scale signatures of unconsciousness are consistent with a departure from critical dynamics
• Dynamical Characteristics of a Hodgkin-Huxley neuron
• Long-range correlations and trends in Colombian seismic time series
• Impact of Tandem Repeats on the Scaling of Nucleotide Sequences
• Long-Term Instrumental and Reconstructed Temperature Records Contradict Anthropogenic Global Warming
• A DFA-based bivariate regression model for estimating the dependence of PM2.5 among neighbouring cities
• Comparative power spectral analysis of simultaneous elecroencephalographic and magnetoencephalographic recordings in humans suggests non-resistive extracellular media
• A Zipf-preserving, long-range correlated surrogate for written language and other symbolic sequences