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On interrelations of recurrences and connectivity trends between stock indices

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  • B. Goswami
  • G. Ambika
  • N. Marwan
  • J. Kurths

Abstract

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.

Suggested Citation

  • B. Goswami & G. Ambika & N. Marwan & J. Kurths, 2011. "On interrelations of recurrences and connectivity trends between stock indices," Papers 1103.5189, arXiv.org.
  • Handle: RePEc:arx:papers:1103.5189
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. Annalisa Fabretti & Marcel Ausloos, 2005. "Recurrence analysis of the NASDAQ crash of April 2000," Papers physics/0505170, arXiv.org.
    4. Bastos, João A. & Caiado, Jorge, 2011. "Recurrence quantification analysis of global stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(7), pages 1315-1325.
    5. 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.
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    Cited by:

    1. Kenett, Dror Y. & Raddant, Matthias & Lux, Thomas & Ben-Jacob, Eshel, 2011. "Evolvement of uniformity and volatility in the stressed global financial village," Kiel Working Papers 1739, Kiel Institute for the World Economy (IfW).
    2. Sandoval, Leonidas Junior, 2013. "To lag or not to lag? How to compare indices of stock markets that operate at different times," Insper Working Papers wpe_319, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.

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