IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v390y2011i21p3670-3678.html
   My bibliography  Save this article

Multifractal Fourier detrended cross-correlation analysis of traffic signals

Author

Listed:
  • Zhao, Xiaojun
  • Shang, Pengjian
  • Lin, Aijing
  • Chen, Gang

Abstract

Multifractal detrended cross-correlation analysis (MF-DXA) has been developed to detect the long-range power-law cross-correlation of considered signals in the presence of non-stationarity. However, crossovers arising from extrinsic periodic trends make the scaling behavior difficult to analyze. We introduce a Fourier filtering method to eliminate the trend effects and systematically investigate the multifractal cross-correlation of simulated and real traffic signals. The crossover locations are found approximately corresponding to the periods of underlying trend. Traffic velocity on one road and flows on adjacent roads show strong cross-correlation. They also present weak multifractality after periodic trends are removed. The traffic velocity and flow are cross-correlated in opposite directions which is accordant to their actual evolution.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:phsmap:v:390:y:2011:i:21:p:3670-3678
    DOI: 10.1016/j.physa.2011.06.018
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437111004651
    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.2011.06.018?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. Shang, Pengjian & Lin, Aijing & Liu, Liang, 2009. "Chaotic SVD method for minimizing the effect of exponential trends in detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(5), pages 720-726.
    2. Nagarajan, Radhakrishnan & Kavasseri, Rajesh G., 2005. "Minimizing the effect of trends on detrended fluctuation analysis of long-range correlated noise," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 182-198.
    3. B. Podobnik & D. F. Fu & H. E. Stanley & P. Ch. Ivanov, 2007. "Power-law autocorrelated stochastic processes with long-range cross-correlations," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 56(1), pages 47-52, March.
    4. Nagarajan, Radhakrishnan, 2006. "Reliable scaling exponent estimation of long-range correlated noise in the presence of random spikes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 366(C), pages 1-17.
    5. Amir Bashan & Ronny Bartsch & Jan W. Kantelhardt & Shlomo Havlin, 2008. "Comparison of detrending methods for fluctuation analysis," Papers 0804.4081, arXiv.org.
    6. B. Podobnik & I. Grosse & D. Horvatić & S. Ilic & P. Ch. Ivanov & H. E. Stanley, 2009. "Quantifying cross-correlations using local and global detrending approaches," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(2), pages 243-250, September.
    7. 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.
    8. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
    9. Chianca, C.V. & Ticona, A. & Penna, T.J.P., 2005. "Fourier-detrended fluctuation analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 357(3), pages 447-454.
    10. Vasiliki Plerou & Parameswaran Gopikrishnan & Bernd Rosenow & Luis A. Nunes Amaral & H. Eugene Stanley, 1999. "Universal and non-universal properties of cross-correlations in financial time series," Papers cond-mat/9902283, arXiv.org.
    11. Shang, Pengjian & Lu, Yongbo & Kamae, Santi, 2008. "Detecting long-range correlations of traffic time series with multifractal detrended fluctuation analysis," Chaos, Solitons & Fractals, Elsevier, vol. 36(1), pages 82-90.
    12. S. Shadkhoo & G. R. Jafari, 2009. "Multifractal detrended cross-correlation analysis of temporal and spatial seismic data," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 72(4), pages 679-683, December.
    13. Sergio Arianos & Anna Carbone, 2008. "Cross-correlation of long-range correlated series," Papers 0804.2064, arXiv.org, revised Mar 2009.
    14. Siqueira, Erinaldo Leite & Stošić, Tatijana & Bejan, Lucian & Stošić, Borko, 2010. "Correlations and cross-correlations in the Brazilian agrarian commodities and stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2739-2743.
    15. Zebende, G.F., 2011. "DCCA cross-correlation coefficient: Quantifying level of cross-correlation," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 614-618.
    16. Zebende, G.F. & Filho, A. Machado, 2009. "Cross-correlation between time series of vehicles and passengers," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(23), pages 4863-4866.
    17. 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.
    18. Podobnik, Boris & Horvatic, Davor & Lam Ng, Alfonso & Eugene Stanley, H. & Ivanov, Plamen Ch., 2008. "Modeling long-range cross-correlations in two-component ARFIMA and FIARCH processes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(15), pages 3954-3959.
    19. Xi-Yuan Qian & Wei-Xing Zhou & Gao-Feng Gu, 2009. "Modified detrended fluctuation analysis based on empirical mode decomposition," Papers 0907.3284, arXiv.org.
    20. Mizuno, Takayuki & Takayasu, Hideki & Takayasu, Misako, 2006. "Correlation networks among currencies," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 364(C), pages 336-342.
    21. L. Kullmann & J. Kertesz & K. Kaski, 2002. "Time dependent cross correlations between different stock returns: A directed network of influence," Papers cond-mat/0203256, arXiv.org, revised May 2002.
    Full references (including those not matched with items on IDEAS)

    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. 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.
    2. Wang, Yudong & Wei, Yu & Wu, Chongfeng, 2011. "Detrended fluctuation analysis on spot and futures markets of West Texas Intermediate crude oil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(5), pages 864-875.
    3. Dutta, Srimonti & Ghosh, Dipak & Samanta, Shukla, 2014. "Multifractal detrended cross-correlation analysis of gold price and SENSEX," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 413(C), pages 195-204.
    4. He, Ling-Yun & Chen, Shu-Peng, 2011. "Nonlinear bivariate dependency of price–volume relationships in agricultural commodity futures markets: A perspective from Multifractal Detrended Cross-Correlation Analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(2), pages 297-308.
    5. Liu, Li-Zhi & Qian, Xi-Yuan & Lu, Heng-Yao, 2010. "Cross-sample entropy of foreign exchange time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(21), pages 4785-4792.
    6. He, Ling-Yun & Chen, Shu-Peng, 2011. "A new approach to quantify power-law cross-correlation and its application to commodity markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3806-3814.
    7. Yang, Yujun & Li, Jianping & Yang, Yimei, 2017. "The cross-correlation analysis of multi property of stock markets based on MM-DFA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 481(C), pages 23-33.
    8. Liu, Li & Wan, Jieqiu, 2011. "A study of correlations between crude oil spot and futures markets: A rolling sample test," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(21), pages 3754-3766.
    9. Zhou, Yu & Chen, Shi, 2016. "Cross-correlation analysis between Chinese TF contracts and treasury ETF based on high-frequency data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 443(C), pages 117-127.
    10. Shi, Wenbin & Shang, Pengjian & Wang, Jing & Lin, Aijing, 2014. "Multiscale multifractal detrended cross-correlation analysis of financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 35-44.
    11. Liu, Li & Wang, Yudong, 2014. "Cross-correlations between spot and futures markets of nonferrous metals," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 400(C), pages 20-30.
    12. Wang, Dong-Hua & Suo, Yuan-Yuan & Yu, Xiao-Wen & Lei, Man, 2013. "Price–volume cross-correlation analysis of CSI300 index futures," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(5), pages 1172-1179.
    13. 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.
    14. 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.
    15. Li, Shuping & Lu, Xinsheng & Li, Jianfeng, 2021. "Cross-correlations between the P2P interest rate, Shibor and treasury yields," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 574(C).
    16. Fan, Qingju & Li, Dan, 2015. "Multifractal cross-correlation analysis in electricity spot market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 429(C), pages 17-27.
    17. Lin, Aijing & Shang, Pengjian & Zhong, Bo, 2014. "Hidden cross-correlation patterns in stock markets based on permutation cross-sample entropy and PCA," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 259-272.
    18. Yanguang Chen, 2015. "A New Methodology of Spatial Cross-Correlation Analysis," PLOS ONE, Public Library of Science, vol. 10(5), pages 1-20, May.
    19. Ladislav Kristoufek, 2014. "Spectrum-based estimators of the bivariate Hurst exponent," Papers 1408.6637, arXiv.org, revised Nov 2014.
    20. Siqueira, Erinaldo Leite & Stošić, Tatijana & Bejan, Lucian & Stošić, Borko, 2010. "Correlations and cross-correlations in the Brazilian agrarian commodities and stocks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(14), pages 2739-2743.

    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:390:y:2011:i:21:p:3670-3678. 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.