IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v388y2009i8p1687-1695.html
   My bibliography  Save this article

On the detection of trends in long-term correlated records

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437108010455
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/j.physa.2008.12.026?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Mantegna,Rosario N. & Stanley,H. Eugene, 2007. "Introduction to Econophysics," Cambridge Books, Cambridge University Press, number 9780521039871, September.
    2. Amir Bashan & Ronny Bartsch & Jan W. Kantelhardt & Shlomo Havlin, 2008. "Comparison of detrending methods for fluctuation analysis," Papers 0804.4081, arXiv.org.
    3. 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.
    4. 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.
    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. 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.
    7. 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.
    8. 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.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Markelov, Oleg & Nguyen Duc, Viet & Bogachev, Mikhail, 2017. "Statistical modeling of the Internet traffic dynamics: To which extent do we need long-term correlations?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 485(C), pages 48-60.
    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.
    5. 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.
    6. Liu, Yanyan & Li, Keping & Yan, Dongyang & Gu, Shuang, 2022. "A network-based CNN model to identify the hidden information in text data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 590(C).
    7. Lu, Feiyu & Yuan, Naiming & Fu, Zuntao & Mao, Jiangyu, 2012. "Universal scaling behaviors of meteorological variables’ volatility and relations with original records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4953-4962.
    8. John Halley & Dimitris Kugiumtzis, 2011. "Nonparametric testing of variability and trend in some climatic records," Climatic Change, Springer, vol. 109(3), pages 549-568, December.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Zhang, Feng & Ren, Hang & Miao, Lijuan & Lei, Yadong & Duan, Mingkeng, 2019. "Simulation of daily precipitation from CMIP5 in the Qinghai-Tibet Plateau," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 15, pages 68-74.
    2. Ni, Xiao-Hui & Jiang, Zhi-Qiang & Gu, Gao-Feng & Ren, Fei & Chen, Wei & Zhou, Wei-Xing, 2010. "Scaling and memory in the non-Poisson process of limit order cancelation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2751-2761.
    3. Santos, José Vicente Cardoso & Perini, Noéle Bissoli & Moret, Marcelo Albano & Nascimento, Erick Giovani Sperandio & Moreira, Davidson Martins, 2021. "Scaling behavior of wind speed in the coast of Brazil and the South Atlantic Ocean: The crossover phenomenon," Energy, Elsevier, vol. 217(C).
    4. Kiyono, Ken & Tsujimoto, Yutaka, 2016. "Nonlinear filtering properties of detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 807-815.
    5. Lu, Feiyu & Yuan, Naiming & Fu, Zuntao & Mao, Jiangyu, 2012. "Universal scaling behaviors of meteorological variables’ volatility and relations with original records," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(20), pages 4953-4962.
    6. Gulich, Damián & Baglietto, Gabriel & Rozenfeld, Alejandro F., 2018. "Temporal correlations in the Vicsek model with vectorial noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 502(C), pages 590-604.
    7. Leonarduzzi, R. & Wendt, H. & Abry, P. & Jaffard, S. & Melot, C. & Roux, S.G. & Torres, M.E., 2016. "p-exponent and p-leaders, Part II: Multifractal analysis. Relations to detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 448(C), pages 319-339.
    8. Hongli Niu & Jun Wang, 2014. "Phase and multifractality analyses of random price time series by finite-range interacting biased voter system," Computational Statistics, Springer, vol. 29(5), pages 1045-1063, October.
    9. Xiong, Gang & Yu, Wenxian & Zhang, Shuning, 2015. "Time-singularity multifractal spectrum distribution based on detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 437(C), pages 351-366.
    10. 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.
    11. Gulich, Damián & Zunino, Luciano, 2014. "A criterion for the determination of optimal scaling ranges in DFA and MF-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 397(C), pages 17-30.
    12. Ruan, Yong-Ping & Zhou, Wei-Xing, 2011. "Long-term correlations and multifractal nature in the intertrade durations of a liquid Chinese stock and its warrant," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(9), pages 1646-1654.
    13. Qian, Xi-Yuan & Gu, Gao-Feng & Zhou, Wei-Xing, 2011. "Modified detrended fluctuation analysis based on empirical mode decomposition for the characterization of anti-persistent processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4388-4395.
    14. Zhao, Xiaojun & Shang, Pengjian & Zhao, Chuang & Wang, Jing & Tao, Rui, 2012. "Minimizing the trend effect on detrended cross-correlation analysis with empirical mode decomposition," Chaos, Solitons & Fractals, Elsevier, vol. 45(2), pages 166-173.
    15. Delignières, Didier & Marmelat, Vivien, 2014. "Strong anticipation and long-range cross-correlation: Application of detrended cross-correlation analysis to human behavioral data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 394(C), pages 47-60.
    16. Xue Pan & Lei Hou & Mutua Stephen & Huijie Yang & Chenping Zhu, 2014. "Evaluation of Scaling Invariance Embedded in Short Time Series," PLOS ONE, Public Library of Science, vol. 9(12), pages 1-27, December.
    17. Klaudia Kozlowska & Miroslaw Latka & Bruce J West, 2020. "Significance of trends in gait dynamics," PLOS Computational Biology, Public Library of Science, vol. 16(10), pages 1-25, October.
    18. Gu, Gao-Feng & Xiong, Xiong & Zhang, Yong-Jie & Chen, Wei & Zhang, Wei & Zhou, Wei-Xing, 2016. "Stylized facts of price gaps in limit order books," Chaos, Solitons & Fractals, Elsevier, vol. 88(C), pages 48-58.
    19. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    20. Nurbanu Bursa & Hüseyin Tatlýdil, 2015. "Investigation of Credit Default Swaps using Detrended Fluctuation Analysis which is an Econophysical Technique," Eurasian Eononometrics, Statistics and Emprical Economics Journal, Eurasian Academy Of Sciences, vol. 2(2), pages 25-33, October.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:phsmap:v:388:y:2009:i:8:p:1687-1695. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.