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Serial Correlation, Periodicity and Scaling of Eigenmodes in an Emerging Market

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  • Diane Wilcox
  • Tim Gebbie
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    Abstract

    We investigate serial correlation, periodic, aperiodic and scaling behaviour of eigenmodes, i.e. daily price fluctuation time-series derived from eigenvectors, of correlation matrices of shares listed on the Johannesburg Stock Exchange (JSE) from January 1993 to December 2002. Periodic, or calendar, components are detected by spectral analysis. We find that calendar effects are limited to eigenmodes which correspond to eigenvalues outside the Wishart range. Using a variance ratio test, we uncover serial correlation in the first eigenmodes and find slight negative serial correlation for eigenmodes within the Wishart range. Our spectral analysis and variance ratio investigations suggest that interpolating missing data or illiquid trading days with zero-order hold introduces high frequency noise and spurious serial correlation. Aperiodic and scaling behaviour of the eigenmodes are investigated by using rescaled-range (R/S) methods and detrended fluctuation analysis (DFA). We find that DFA and classic and modified R/S exponents suggest the presence of long-term memory effects in the first five eigenmodes.

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    File URL: http://arxiv.org/pdf/cond-mat/0404416
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    Bibliographic Info

    Paper provided by arXiv.org in its series Papers with number cond-mat/0404416.

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    Date of creation: Apr 2004
    Date of revision: Sep 2007
    Publication status: Published in IJTAF, 11, 7 (November 2008), pp. 739-760
    Handle: RePEc:arx:papers:cond-mat/0404416

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    Web page: http://arxiv.org/

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    1. S. Drozdz & J. Kwapien & F. Gruemmer & F. Ruf & J. Speth, 2001. "Quantifying dynamics of the financial correlations," Papers cond-mat/0102402, arXiv.org.
    2. Stefano Galluccio & Jean-Philippe Bouchaud & Marc Potters, 1998. "Rational decisions, random matrices and spin glasses," Science & Finance (CFM) working paper archive 500054, Science & Finance, Capital Fund Management.
    3. Drożdż, S. & Kwapień, J. & Grümmer, F. & Ruf, F. & Speth, J., 2001. "Quantifying the dynamics of financial correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 299(1), pages 144-153.
    4. Ross, Stephen A., 1976. "The arbitrage theory of capital asset pricing," Journal of Economic Theory, Elsevier, Elsevier, vol. 13(3), pages 341-360, December.
    5. Galluccio, Stefano & Bouchaud, Jean-Philippe & Potters, Marc, 1998. "Rational decisions, random matrices and spin glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, Elsevier, vol. 259(3), pages 449-456.
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