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Detrended Multiple Cross-Correlation Coefficient

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  • Zebende, G.F.
  • da Silva Filho, A.M.

Abstract

Based on the detrended cross-correlation coefficient, ρxa,xb, we propose in this paper to establish a Detrended Multiple Cross-Correlation coefficient, DMCx2, to be applied in order to quantify the relations between non-stationary signals on different time scales. This Detrended Multiple Cross-Correlation coefficient will be the measure of the total association between the dependent variable, y, with the others i independent variables, x. It will be the generalization of ρxa,xb, for more than two independent variables. To validate DMCx2, we set up a cross-correlation table (ranging from 0 to 1), and we determined the Detrended Multiple Cross-Correlation coefficient into simulated and real time series. The results of this analysis show that the Detrended Multiple Cross-Correlation coefficient may be suitable and useful to measure multiple cross-correlations, as we will see in this paper.

Suggested Citation

  • Zebende, G.F. & da Silva Filho, A.M., 2018. "Detrended Multiple Cross-Correlation Coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 510(C), pages 91-97.
    • Handle: RePEc:eee:phsmap:v:510:y:2018:i:c:p:91-97
    DOI: 10.1016/j.physa.2018.06.119
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    References listed on IDEAS

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    1. da Silva, Marcus Fernandes & de Area Leão Pereira, Éder Johnson & da Silva Filho, Aloisio Machado & de Castro, Arleys Pereira Nunes & Miranda, José Garcia Vivas & Zebende, Gilney Figueira, 2016. "Quantifying the contagion effect of the 2008 financial crisis between the G7 countries (by GDP nominal)," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 453(C), pages 1-8.
    2. Milton Friedman, 1962. "Introduction to "The Interpolation of Time Series by Related Series"," NBER Chapters, in: The Interpolation of Time Series by Related Series, pages 1-3, National Bureau of Economic Research, Inc.
    3. Bashir, Usman & Yu, Yugang & Hussain, Muntazir & Zebende, Gilney F., 2016. "Do foreign exchange and equity markets co-move in Latin American region? Detrended cross-correlation approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 889-897.
    4. Vassoler, R.T. & Zebende, G.F., 2012. "DCCA cross-correlation coefficient apply in time series of air temperature and air relative humidity," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2438-2443.
    5. Milton Friedman, 1962. "The Interpolation of Time Series by Related Series," NBER Books, National Bureau of Economic Research, Inc, number frie62-1.
    6. Wang, Gang-Jin & Xie, Chi & Chen, Shou & Yang, Jiao-Jiao & Yang, Ming-Yan, 2013. "Random matrix theory analysis of cross-correlations in the US stock market: Evidence from Pearson’s correlation coefficient and detrended cross-correlation coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(17), pages 3715-3730.
    7. Zebende, G.F. & da Silva, M.F. & Machado Filho, A., 2013. "DCCA cross-correlation coefficient differentiation: Theoretical and practical approaches," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(8), pages 1756-1761.
    8. Pawe{l} O'swic{e}cimka & Stanis{l}aw Dro.zd.z & Marcin Forczek & Stanis{l}aw Jadach & Jaros{l}aw Kwapie'n, 2013. "Detrended Cross-Correlation Analysis Consistently Extended to Multifractality," Papers 1308.6148, arXiv.org, revised Feb 2014.
    9. Gvozdanovic, Igor & Podobnik, Boris & Wang, Duan & Eugene Stanley, H., 2012. "1/f behavior in cross-correlations between absolute returns in a US market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(9), pages 2860-2866.
    10. Reboredo, Juan Carlos & Rivera-Castro, Miguel A. & Zebende, Gilney F., 2014. "Oil and US dollar exchange rate dependence: A detrended cross-correlation approach," Energy Economics, Elsevier, vol. 42(C), pages 132-139.
    11. Zhi-Qiang Jiang & Wei-Xing Zhou, 2011. "Multifractal detrending moving average cross-correlation analysis," Papers 1103.2577, arXiv.org, revised Mar 2011.
    12. Xi-Yuan Qian & Ya-Min Liu & Zhi-Qiang Jiang & Boris Podobnik & Wei-Xing Zhou & H. Eugene Stanley, 2015. "Detrended partial cross-correlation analysis of two nonstationary time series influenced by common external forces," Papers 1504.02435, arXiv.org, revised Apr 2015.
    13. 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.
    14. Wei-Xing Zhou, 2008. "Multifractal detrended cross-correlation analysis for two nonstationary signals," Papers 0803.2773, arXiv.org.
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    17. da Silva Filho, A.M. & Zebende, G.F. & de Castro, A.P.N. & Guedes, E.F., 2021. "Statistical test for Multiple Detrended Cross-Correlation Coefficient," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 562(C).

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