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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. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871.
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    Cited by:

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    2. Viola, Flavio M. & Paiva, Susana L.D. & Savi, Marcelo A., 2010. "Analysis of the global warming dynamics from temperature time series," Ecological Modelling, Elsevier, vol. 221(16), pages 1964-1978.
    3. Schumann, Aicko Y. & Kantelhardt, Jan W., 2011. "Multifractal moving average analysis and test of multifractal model with tuned correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(14), pages 2637-2654.
    4. Setty, V.A. & Sharma, A.S., 2015. "Characterizing Detrended Fluctuation Analysis of multifractional Brownian motion," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 419(C), pages 698-706.
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    6. Hatem A. Ewea & Nassir S. Al-Amri & Mohamed A. Dawoud & Amro M. Elfeki, 2018. "Developing models and envelope curves for extreme floods in the Saudi Arabia arid environment," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 94(2), pages 801-817, November.
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