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On the detection of trends in long-term correlated records

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  • Rybski, Diego
  • Bunde, Armin

Abstract

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 differently by trends. For a given instrumental record of length N, we compare the fluctuation exponent α0 of DFA0 where trends are not being eliminated, with the fluctuation exponent α2 of DFA2 where possible linear trends in the instrumental record are being eliminated. From this we deduce numerically the probability density p(A) that in the considered long-term correlated record, a linear trend with a slope between A and A+dA occurs. Without loss of generality we focus on Gaussian distributed data. As an example, we apply our analysis to several long temperature records (Melbourne, Oxford, Prague, Pusan, Uppsala, and Vienna), where we discuss the trends within the last 90 years, which may originate from both, urban and global warming.

Suggested Citation

  • Rybski, Diego & Bunde, Armin, 2009. "On the detection of trends in long-term correlated records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1687-1695.
    • Handle: RePEc:eee:phsmap:v:388:y:2009:i:8:p:1687-1695
    DOI: 10.1016/j.physa.2008.12.026
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    References listed on IDEAS

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    1. Monetti, Roberto A. & Havlin, Shlomo & Bunde, Armin, 2003. "Long-term persistence in the sea surface temperature fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 581-589.
    2. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, October.
    3. Vjushin, Dmitry & Govindan, R.B. & Monetti, Roberto A. & Havlin, Shlomo & Bunde, Armin, 2001. "Scaling analysis of trends using DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 302(1), pages 234-243.
    4. Amir Bashan & Ronny Bartsch & Jan W. Kantelhardt & Shlomo Havlin, 2008. "Comparison of detrending methods for fluctuation analysis," Papers 0804.4081, arXiv.org.
    5. Koscielny-Bunde, Eva & Bunde, Armin & Havlin, Shlomo & Goldreich, Yair, 1996. "Analysis of daily temperature fluctuations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 231(4), pages 393-396.
    6. Kantelhardt, Jan W. & Zschiegner, Stephan A. & Koscielny-Bunde, Eva & Havlin, Shlomo & Bunde, Armin & Stanley, H.Eugene, 2002. "Multifractal detrended fluctuation analysis of nonstationary time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 87-114.
    7. Kantelhardt, Jan W & Koscielny-Bunde, Eva & Rego, Henio H.A & Havlin, Shlomo & Bunde, Armin, 2001. "Detecting long-range correlations with detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 295(3), pages 441-454.
    8. Bashan, Amir & Bartsch, Ronny & Kantelhardt, Jan W. & Havlin, Shlomo, 2008. "Comparison of detrending methods for fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5080-5090.
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