Detecting long-range correlations with detrended fluctuation analysis

2001/02/12 by Jan W. Kantelhardt, Eva Koscielny–Bunde, Eva Koscielny-Bunde +4 · 15 citations
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Physics and Astronomy · #Chaos control and synchronization #Complex Systems and Time Series Analysis #Fractal and DNA sequence analysis #cond-mat.stat-mech

paper · pdf · doi:10.1016/s0378-4371(01)00144-3

published as Physica A 295, 441-454 (2001) · 10 pages, including 8 figures

arxiv created 2001/02/12 · openalex publication_date 2001/06/01 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/03

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.

Citations

• Mosaic organization of DNA nucleotides
• Method for Generating Long-Range Correlations for Large Systems
• Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series

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