Detecting Long-Range Correlations with Detrended Fluctuation Analysis. Kantelhardt, J. W.; Koscielny-Bunde, E.; Rego, H. H. A.; Havlin, S.; and Bunde, A. 295(3-4):441–454.
Detecting Long-Range Correlations with Detrended Fluctuation Analysis [link]Paper  doi  abstract   bibtex   
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.
@article{kantelhardtDetectingLongrangeCorrelations2001,
  title = {Detecting Long-Range Correlations with Detrended Fluctuation Analysis},
  author = {Kantelhardt, Jan W. and Koscielny-Bunde, Eva and Rego, Henio H. A. and Havlin, Shlomo and Bunde, Armin},
  date = {2001-06},
  journaltitle = {Physica A: Statistical Mechanics and its Applications},
  volume = {295},
  pages = {441--454},
  issn = {0378-4371},
  doi = {10.1016/s0378-4371(01)00144-3},
  url = {https://doi.org/10.1016/s0378-4371(01)00144-3},
  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 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.},
  keywords = {*imported-from-citeulike-INRMM,~INRMM-MiD:c-14284063,bias-correction,correlation-analysis,data-transformation-modelling,mathematics,modelling,statistics},
  number = {3-4}
}
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