Detecting long-range correlations with detrended fluctuation analysis

  title={Detecting long-range correlations with detrended fluctuation analysis},
  author={J. Kantelhardt and E. Koscielny-Bunde and H. A. Rego and S. Havlin and A. Bunde},
  journal={Physica A-statistical Mechanics and Its Applications},
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 which 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… Expand

Figures from this paper

Minimizing the effect of exponential trends in detrended fluctuation analysis
Abstract The detrended fluctuation analysis (DFA) and its extensions (MF-DFA) have been used extensively to determine possible long-range correlations in time series. However, recent studies haveExpand
Comparison of detrending methods for fluctuation analysis
We examine several recently suggested methods for the detection of long-range correlations in data series based on similar ideas as the well-established Detrended Fluctuation Analysis (DFA). InExpand
Minimizing the Effect of sinusoidal Trends in Detrended Fluctuation Analysis
A smoothing filter is proposed to minimize the effect of sinusoidal trends and distortion in the log–log plots obtained by DFA and MF-DFA techniques. Expand
Detrending fluctuation analysis based on moving average filtering
Abstract Detrended fluctuation analysis (DFA) is a scaling method commonly used for detecting long-range correlations in nonstationary time series. Applications range from financial time series toExpand
On the detection of trends in long-term correlated records
We use the Detrended Fluctuation Analysis (DFA) to quantify underlying trends in long-term correlated records. Our approach is based on the fact that different orders of DFA are affected differentlyExpand
Scaling analysis of trends using DFA
We study two aspects of the detrended fluctuation analysis (DFA) method, namely the scaling behavior of the leading terms of the best-fit polynomials and the detection of trends. We show analyticallyExpand
Effect of the signal filtering on detrended fluctuation analysis
Abstract Detrended fluctuation analysis (DFA) is an effective method to accurately quantify long-term correlations embedded in a nonstationary time series. In this paper, we study the effect ofExpand
The fluctuation function of the detrended fluctuation analysis — investigation on the AR(1) process
We derive an analytical expression for the fluctuation function of the first order autoregressive process AR(1) by means of the detrended fluctuation analysis (DFA). This process is short-rangeExpand
Theoretical foundation of detrending methods for fluctuation analysis such as detrended fluctuation analysis and detrending moving average.
Basic principles for detrended fluctuation analysis and detrending moving average methods are claimed, where DFA and DMA are then shown to be specific realizations. Expand
The Detrended Fluctuation Analysis (DFA) and its extensions (MF-DFA) have been proposed as robust techniques to determine possible long-range correlations in self-affine signals. However, manyExpand


Application of the detrended fluctuation analysis (DFA) method for describing cloud breaking
A method to sort out correlations and decorrelations in stratus cloud formation, persistence and breakup is introduced. The detrended fluctuation analysis (DFA) statistical method is applied toExpand
Power spectrum and detrended fluctuation analysis: application to daily temperatures
  • Talkner, Weber
  • Mathematics, Medicine
  • Physical 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. Expand
Deviations from uniform power law scaling in nonstationary time series.
This work test the hypothesis that the scaling properties of the dynamics of healthy physiological systems are more stable than those of pathological systems by studying beat-to-beat fluctuations in the human heart rate, and develops techniques based on the Fano factor and Allan factor functions for quantifying deviations from uniform power-law scaling in nonstationary time series. Expand
Long-range anticorrelations and non-Gaussian behavior of the heartbeat.
It is found that the successive increments in the cardiac beat-to-beat intervals of healthy subjects display scale-invariant, long-range anticorrelations (up to 10(4) heart beats), and the different scaling behavior in health and disease must relate to the underlying dynamics of the heartbeat. Expand
We investigate the local cumulative phases at single sites of the lattice for time-dependent wave functions in the Anderson model in d=2 and 3. In addition to a local linear trend, the phases exhibitExpand
Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series.
A new method--detrended fluctuation analysis (DFA)--for quantifying this correlation property in non-stationary physiological time series is described and application of this technique shows evidence for a crossover phenomenon associated with a change in short and long-range scaling exponents. Expand
Indication of a Universal Persistence Law Governing Atmospheric Variability
We study the temporal correlations in the atmospheric variability by 14 meteorological stations around the globe, the variations of the daily maximum temperatures from their average values. We applyExpand
Detrended fluctuation analysis of time series of a firing fusimotor neuron
We study the interspike intervals (ISI) time series of the spontaneous fusimotor neuron activity by applying the detrended fluctuation analysis that is a modification of the random walk modelExpand
The correlation function of a financial index of the New York stock exchange, the S&P 500, is analyzed at 1 min intervals over the 13-year period, Jan 84 -- Dec 96. We quantify the correlations ofExpand
Applications of statistical physics to economic and financial topics
Problems in economy and finance have started to attract the interest of statistical physicists. Fundamental problems pertain to the existence or not of long-, medium-, short-range power-lawExpand