IDEAS home Printed from https://ideas.repec.org/p/arx/papers/cond-mat-0404416.html
   My bibliography  Save this paper

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

Author

Listed:
  • Diane Wilcox
  • Tim Gebbie

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.

Suggested Citation

  • Diane Wilcox & Tim Gebbie, 2004. "Serial Correlation, Periodicity and Scaling of Eigenmodes in an Emerging Market," Papers cond-mat/0404416, arXiv.org, revised Sep 2007.
    • Handle: RePEc:arx:papers:cond-mat/0404416
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/cond-mat/0404416
    File Function: Latest version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Stephen A. Ross, 2013. "The Arbitrage Theory of Capital Asset Pricing," World Scientific Book Chapters, in: Leonard C MacLean & William T Ziemba (ed.), HANDBOOK OF THE FUNDAMENTALS OF FINANCIAL DECISION MAKING Part I, chapter 1, pages 11-30, World Scientific Publishing Co. Pte. Ltd..
    2. Drożdż, S & Kwapień, J & Speth, J & Wójcik, M, 2002. "Identifying complexity by means of matrices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 314(1), pages 355-361.
    3. Galluccio, Stefano & Bouchaud, Jean-Philippe & Potters, Marc, 1998. "Rational decisions, random matrices and spin glasses," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 259(3), pages 449-456.
    4. S. Drozdz & J. Kwapien & F. Gruemmer & F. Ruf & J. Speth, 2001. "Quantifying dynamics of the financial correlations," Papers cond-mat/0102402, arXiv.org.
    5. 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, vol. 299(1), pages 144-153.
    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. Diane Wilcox & Tim Gebbie, 2004. "An analysis of Cross-correlations in South African Market data," Papers cond-mat/0402389, arXiv.org, revised Sep 2006.
    2. Wilcox, Diane & Gebbie, Tim, 2007. "An analysis of cross-correlations in an emerging market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 375(2), pages 584-598.
    3. Marcin Wk{a}torek & Stanis{l}aw Dro.zd.z & Jaros{l}aw Kwapie'n & Ludovico Minati & Pawe{l} O'swik{e}cimka & Marek Stanuszek, 2020. "Multiscale characteristics of the emerging global cryptocurrency market," Papers 2010.15403, arXiv.org, revised Mar 2021.
    4. Marsili, Matteo & Raffaelli, Giacomo & Ponsot, Benedicte, 2009. "Dynamic instability in generic model of multi-assets markets," Journal of Economic Dynamics and Control, Elsevier, vol. 33(5), pages 1170-1181, May.
    5. Nobi, Ashadun & Lee, Jae Woo, 2016. "State and group dynamics of world stock market by principal component analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 450(C), pages 85-94.
    6. Stephan Süss, 2012. "The pricing of idiosyncratic risk: evidence from the implied volatility distribution," Financial Markets and Portfolio Management, Springer;Swiss Society for Financial Market Research, vol. 26(2), pages 247-267, June.
    7. Wilcox, Diane & Gebbie, Tim, 2004. "On the analysis of cross-correlations in South African market data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 344(1), pages 294-298.
    8. Münnix, Michael C. & Schäfer, Rudi, 2011. "A copula approach on the dynamics of statistical dependencies in the US stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(23), pages 4251-4259.
    9. Eckrot, A. & Jurczyk, J. & Morgenstern, I., 2016. "Ising model of financial markets with many assets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 462(C), pages 250-254.
    10. Ormerod, Paul & Mounfield, Craig, 2002. "The convergence of European business cycles 1978–2000," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 307(3), pages 494-504.
    11. Kwapień, J. & Drożdż, S. & Grümmer, F. & Ruf, F. & Speth, J., 2002. "Decomposing the stock market intraday dynamics," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 309(1), pages 171-182.
    12. Roehner, Bertrand M., 2005. "Stock markets are not what we think they are: the key roles of cross-ownership and corporate treasury stock," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 347(C), pages 613-625.
    13. Stanis{l}aw Dro.zd.z & Rafa{l} Kowalski & Pawe{l} O'swic{e}cimka & Rafa{l} Rak & Robert Gc{e}barowski, 2018. "Dynamical variety of shapes in financial multifractality," Papers 1809.06728, arXiv.org.
    14. Marcin Wk{a}torek & Jaros{l}aw Kwapie'n & Stanis{l}aw Dro.zd.z, 2021. "Financial Return Distributions: Past, Present, and COVID-19," Papers 2107.06659, arXiv.org.
    15. Baoqiang Zhan & Shu Zhang & Helen S. Du & Xiaoguang Yang, 2022. "Exploring Statistical Arbitrage Opportunities Using Machine Learning Strategy," Computational Economics, Springer;Society for Computational Economics, vol. 60(3), pages 861-882, October.
    16. Shi, Huai-Long & Zhou, Wei-Xing, 2022. "Factor volatility spillover and its implications on factor premia," Journal of International Financial Markets, Institutions and Money, Elsevier, vol. 80(C).
    17. Bonhomme, Stphane & Robin, Jean-Marc, 2009. "Consistent noisy independent component analysis," Journal of Econometrics, Elsevier, vol. 149(1), pages 12-25, April.
    18. Andros Gregoriou & Christos Ioannidis, 2007. "Generalized method of moments and present value tests of the consumption-capital asset pricing model under transactions costs: evidence from the UK stock market," Empirical Economics, Springer, vol. 32(1), pages 19-39, April.
    19. David E. Allen & Michael McAleer & Abhay K. Singh, 2019. "Daily market news sentiment and stock prices," Applied Economics, Taylor & Francis Journals, vol. 51(30), pages 3212-3235, June.
    20. Sellin, Peter, 1998. "Monetary Policy and the Stock Market: Theory and Empirical Evidence," Working Paper Series 72, Sveriges Riksbank (Central Bank of Sweden).

    More about this item

    Statistics

    Access and download statistics

    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:arx:papers:cond-mat/0404416. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.org/ .

    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.