Detecting long-range correlations with detrended fluctuation analysis

By Jan W. Kantelhardt, Eva Koscielny-Bunde, H. A. Rego, Shlomo Havlin, Armin Bunde. 2001

1,327 citations recorded by the source corpus.

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 reliably and determined quantitatively and show how several types of trends in the data affect the different orders of DFA.

Subfields: Economics and Econometrics, Molecular Biology, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9af88051f5e96ce50a456f198908e18c83f1a4e6

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Citations in the corpus

A multifractal description of wind speed records (2004, background): “Polynomial detrending of order m is capable of eliminating trends up to order m-1. [ 23 ]”
A modified method for detecting incipient bifurcations in a dynamical system (2007, background): “For uncorrelated records, a = 0.5, while for long-term correlated (persistent) records, a > 0.5 [Kantelhardt et al., 2001].”
Temporal correlations and clustering of landslides (2010, methodology): “Another popular technique to examine correlations in a time series is detrended fl uctuation analysis (DFA) (Peng et al., 1992, Kantelhardt et al., 2001) where the average variation per time scale is evaluated.”
Long-term persistence in the sea surface temperature fluctuations (2002, methodology): “In this Letter, we study the persistence in sea surface temperature (SST) records at many sites in the Atlantic and Pacific oceans using the detrended fluctuation analysis (DFA) method [Peng et al., 1994; Kantelhardt et al., 2001].”
Detrended Fluctuation Analysis: A Scale-Free View on Neuronal Oscillations (2012, methodology): “Other trend-removal techniques have been proposed, such as higher-order polynomial (Kantelhardt et al., 2001) or adaptive detrending (Riley et al., 2012); however, these have not yet been tested in the DFA analysis of neuronal oscillations.”
Switchbacks in the Near-Sun Magnetic Field: Long Memory and Impact on the Turbulence Cascade (2019, background): “To better diagnose the origin of this long memory let us now consider Detrended Fluctuation Analysis (DFA) [10, 30], which is particularly suited for detecting long memory in non-stationary time series.”
Trend evaluation in records with long‐term memory: Application to global warming (2009, methodology): “To determine a, we use 2nd order detrended fluctuation analysis (DFA2 [see, e.g., Kantelhardt et al., 2001 ]), where linear trends in the data are being removed systematically.”
Multifractality in combustion noise: predicting an impending combustion instability (2014, methodology): “Detrended fluctuation analysis (DFA) (Peng et al. 1994) provides an easy approach to characterize fractality in a given time series data.”
Tempting long-memory - on the interpretation of DFA results (2004, background): “The ability of DFA to estimateα from realizations of long-memory processes corrupted by different instationarities like trends, spikes, harmonics and gaps has been studied byHu et al.(2001), Chen et al.(2002) and Kantelhardt et al.(2001).”