IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v41y2009i1p311-316.html
   My bibliography  Save this article

Minimizing the effect of exponential trends in detrended fluctuation analysis

Author

Listed:
  • Xu, Na
  • Shang, Pengjian
  • Kamae, Santi

Abstract

The detrended fluctuation analysis (DFA) and its extensions (MF-DFA) have been used extensively to determine possible long-range correlations in time series. However, recent studies have reported the susceptibility of DFA to trends which give rise to spurious crossovers and prevent reliable estimation of the scaling exponents. In this report, a smoothing algorithm based on the discrete laplace transform (DFT) is proposed to minimize the effect of exponential trends and distortion in the log–log plots obtained by MF-DFA techniques. The effectiveness of the technique is demonstrated on monofractal and multifractal data corrupted with exponential trends.

Suggested Citation

  • Xu, Na & Shang, Pengjian & Kamae, Santi, 2009. "Minimizing the effect of exponential trends in detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 311-316.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:311-316
    DOI: 10.1016/j.chaos.2007.12.006
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077907009836
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2007.12.006?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. Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of periodic and quasi-periodic trends in detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 777-784.
    2. Morariu, V.V. & Isvoran, Adriana & Zainea, Oana, 2007. "A non-linear approach to the structure–mobility relationship in protein main chains," Chaos, Solitons & Fractals, Elsevier, vol. 32(4), pages 1305-1315.
    3. Vitanov, Nikolay K. & Yankulova, Elka D., 2006. "Multifractal analysis of the long-range correlations in the cardiac dynamics of Drosophila melanogaster," Chaos, Solitons & Fractals, Elsevier, vol. 28(3), pages 768-775.
    4. Kavasseri, Rajesh G. & Nagarajan, Radhakrishnan, 2005. "A multifractal description of wind speed records," Chaos, Solitons & Fractals, Elsevier, vol. 24(1), pages 165-173.
    5. Telesca, Luciano & Balasco, Marianna & Lapenna, Vincenzo, 2007. "Investigating the time-correlation properties in self-potential signals recorded in a seismic area of Irpinia, southern Italy," Chaos, Solitons & Fractals, Elsevier, vol. 32(1), pages 199-211.
    6. Silva, F.E. & Gonçalves, L.L. & Fereira, D.B.B. & Rebello, J.M.A., 2005. "Characterization of failure mechanism in composite materials through fractal analysis of acoustic emission signals," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 481-494.
    7. 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.
    8. Gerhardt, Günther J.L. & Lemke, Ney & Corso, Gilberto, 2006. "Network clustering coefficient approach to DNA sequence analysis," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 1037-1045.
    9. Currenti, Gilda & Negro, Ciro Del & Lapenna, Vincenzo & Telesca, Luciano, 2005. "Fluctuation analysis of the hourly time variability of volcano-magnetic signals recorded at Mt. Etna Volcano, Sicily (Italy)," Chaos, Solitons & Fractals, Elsevier, vol. 23(5), pages 1921-1929.
    10. Peng, C.-K. & Buldyrev, S.V. & Goldberger, A.L. & Havlin, S. & Mantegna, R.N. & Simons, M. & Stanley, H.E., 1995. "Statistical properties of DNA sequences," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 221(1), pages 180-192.
    11. 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. Chi Zhang & Zhengning Pu & Qin Zhou, 2018. "Sustainable Energy Consumption in Northeast Asia: A Case from China’s Fuel Oil Futures Market," Sustainability, MDPI, vol. 10(1), pages 1-14, January.
    2. Lucheng Hong & Wantao Shu & Angela C. Chao, 2018. "Recurrence Interval Analysis on Electricity Consumption of an Office Building in China," Sustainability, MDPI, vol. 10(2), pages 1-15, January.
    3. 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.
    4. Zhao, Xiaojun & Shang, Pengjian & Lin, Aijing & Chen, Gang, 2011. "Multifractal Fourier detrended cross-correlation analysis of traffic signals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3670-3678.
    5. Jiang, Zhi-Qiang & Xie, Wen-Jie & Zhou, Wei-Xing, 2014. "Testing the weak-form efficiency of the WTI crude oil futures market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 405(C), pages 235-244.
    6. Yin, Yi & Shang, Pengjian & Ahn, Andrew C. & Peng, Chung-Kang, 2019. "Multiscale joint permutation entropy for complex time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 515(C), pages 388-402.
    7. Xie, Wen-Jie & Jiang, Zhi-Qiang & Zhou, Wei-Xing, 2014. "Extreme value statistics and recurrence intervals of NYMEX energy futures volatility," Economic Modelling, Elsevier, vol. 36(C), pages 8-17.
    8. Li, Hongtao & Gedikli, Ersegun Deniz & Lubbad, Raed, 2020. "Exploring time-delay-based numerical differentiation using principal component analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 556(C).

    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. Ausloos, M., 2012. "Measuring complexity with multifractals in texts. Translation effects," Chaos, Solitons & Fractals, Elsevier, vol. 45(11), pages 1349-1357.
    2. Vitanov, Nikolay K. & Sakai, Kenshi & Dimitrova, Zlatinka I., 2008. "SSA, PCA, TDPSC, ACFA: Useful combination of methods for analysis of short and nonstationary time series," Chaos, Solitons & Fractals, Elsevier, vol. 37(1), pages 187-202.
    3. Jiang, Lei & Zhang, Jiping & Liu, Xinwei & Li, Fei, 2016. "Multi-fractal scaling comparison of the Air Temperature and the Surface Temperature over China," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 783-792.
    4. Jamshid Ardalankia & Mohammad Osoolian & Emmanuel Haven & G. Reza Jafari, 2019. "Scaling Features of Price-Volume Cross-Correlation," Papers 1903.01744, arXiv.org, revised Aug 2020.
    5. Kalamaras, N. & Philippopoulos, K. & Deligiorgi, D. & Tzanis, C.G. & Karvounis, G., 2017. "Multifractal scaling properties of daily air temperature time series," Chaos, Solitons & Fractals, Elsevier, vol. 98(C), pages 38-43.
    6. Vitanov, Nikolay K. & Hoffmann, Norbert P. & Wernitz, Boris, 2014. "Nonlinear time series analysis of vibration data from a friction brake: SSA, PCA, and MFDFA," Chaos, Solitons & Fractals, Elsevier, vol. 69(C), pages 90-99.
    7. Gajardo, Gabriel & Kristjanpoller, Werner D. & Minutolo, Marcel, 2018. "Does Bitcoin exhibit the same asymmetric multifractal cross-correlations with crude oil, gold and DJIA as the Euro, Great British Pound and Yen?," Chaos, Solitons & Fractals, Elsevier, vol. 109(C), pages 195-205.
    8. Ardalankia, Jamshid & Osoolian, Mohammad & Haven, Emmanuel & Jafari, G. Reza, 2020. "Scaling features of price–volume cross correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 549(C).
    9. de Oliveira Santos, Maíra & Stosic, Tatijana & Stosic, Borko D., 2012. "Long-term correlations in hourly wind speed records in Pernambuco, Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1546-1552.
    10. Zunino, Luciano & Figliola, Alejandra & Tabak, Benjamin M. & Pérez, Darío G. & Garavaglia, Mario & Rosso, Osvaldo A., 2009. "Multifractal structure in Latin-American market indices," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2331-2340.
    11. Pavón-Domínguez, P. & Serrano, S. & Jiménez-Hornero, F.J. & Jiménez-Hornero, J.E. & Gutiérrez de Ravé, E. & Ariza-Villaverde, A.B., 2013. "Multifractal detrended fluctuation analysis of sheep livestock prices in origin," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4466-4476.
    12. Tzanis, Chris G. & Kalamaras, Nikolaos & Philippopoulos, Kostas & Deligiorgi, Despina, 2022. "The multifractal nature of dew point," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    13. Lavička, Hynek & Kracík, Jiří, 2020. "Fluctuation analysis of electric power loads in Europe: Correlation multifractality vs. Distribution function multifractality," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    14. El Alaoui, Marwane & Benbachir, Saâd, 2013. "Multifractal detrended cross-correlation analysis in the MENA area," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(23), pages 5985-5993.
    15. Méndez-Gordillo, Alma Rosa & Cadenas, Erasmo, 2021. "Wind speed forecasting by the extraction of the multifractal patterns of time series through the multiplicative cascade technique," Chaos, Solitons & Fractals, Elsevier, vol. 143(C).
    16. Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of periodic and quasi-periodic trends in detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 26(3), pages 777-784.
    17. Stosic, Tatijana & Telesca, Luciano & Stosic, Borko, 2021. "Multiparametric statistical and dynamical analysis of angular high-frequency wind speed time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 566(C).
    18. Laura Raisa Miloş & Cornel Haţiegan & Marius Cristian Miloş & Flavia Mirela Barna & Claudiu Boțoc, 2020. "Multifractal Detrended Fluctuation Analysis (MF-DFA) of Stock Market Indexes. Empirical Evidence from Seven Central and Eastern European Markets," Sustainability, MDPI, vol. 12(2), pages 1-15, January.
    19. 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.
    20. Zhou, Yu & Leung, Yee & Ma, Jian-Min, 2013. "Empirical study of the scaling behavior of the amplitude–frequency distribution of the Hilbert–Huang transform and its application in sunspot time series analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(6), pages 1336-1346.

    More about this item

    Statistics

    Access and download statistics

    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:chsofr:v:41:y:2009:i:1:p:311-316. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.