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On interrelations of recurrences and connectivity trends between stock indices

  • B. Goswami
  • G. Ambika
  • N. Marwan
  • J. Kurths
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    Financial data has been extensively studied for correlations using Pearson's cross-correlation coefficient {\rho} as the point of departure. We employ an estimator based on recurrence plots --- the Correlation of Probability of Recurrence (CPR) --- to analyze connections between nine stock indices spread worldwide. We suggest a slight modification of the CPR approach in order to get more robust results. We examine trends in CPR for an approximately 19-month window moved along the time series and compare them to {\rho}. Binning CPR into three levels of connectedness: strong, moderate and weak, we extract the trends in number of connections in each bin over time. We also look at the behavior of CPR during the Dot-Com bubble by shifting the time series to align their peaks. CPR mainly uncovers that the markets move in and out of periods of strong connectivity erratically, instead of moving monotonously towards increasing global connectivity. This is in contrast to {\rho}, which gives a picture of ever increasing correlation. CPR also exhibits that time shifted markets have high connectivity around the Dot-Com bubble of 2000. We stress on the importance of significance testing in interpreting measures applied to field data. CPR is more robust to significance testing. It has the additional advantages of being robust to noise, and reliable for short time series lengths and low frequency of sampling. Further, it is more sensitive to changes than {\rho} as it captures correlations between the essential dynamics of the underlying systems.

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    File URL: http://arxiv.org/pdf/1103.5189
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    Paper provided by arXiv.org in its series Papers with number 1103.5189.

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    Date of creation: Mar 2011
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    Publication status: Published in Physica A, 391, 4364 (2012)
    Handle: RePEc:arx:papers:1103.5189
    Contact details of provider: Web page: http://arxiv.org/

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    1. Annalisa Fabretti & Marcel Ausloos, 2005. "Recurrence analysis of the NASDAQ crash of April 2000," Papers physics/0505170, arXiv.org.
    2. Joao A. Bastos & Jorge Caiado, 2010. "Recurrence quantification analysis of global stock markets," CEMAPRE Working Papers 1006, Centre for Applied Mathematics and Economics (CEMAPRE), School of Economics and Management (ISEG), Technical University of Lisbon.
    3. Marc Potters & Jean-Philippe Bouchaud, 2001. "More stylized facts of financial markets: leverage effect and downside correlations," Science & Finance (CFM) working paper archive 29960, Science & Finance, Capital Fund Management.
    4. Granger, C. W. J., 1981. "Some properties of time series data and their use in econometric model specification," Journal of Econometrics, Elsevier, vol. 16(1), pages 121-130, May.
    5. Coelho, Ricardo & Gilmore, Claire G. & Lucey, Brian & Richmond, Peter & Hutzler, Stefan, 2007. "The evolution of interdependence in world equity markets—Evidence from minimum spanning trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 455-466.
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