IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v287y2000i3p362-373.html
   My bibliography  Save this article

Scaling and correlation in financial time series

Author

Listed:
  • Gopikrishnan, P
  • Plerou, V
  • Liu, Y
  • Amaral, L.A.N
  • Gabaix, X
  • Stanley, H.E

Abstract

We discuss the results of three recent phenomenological studies focussed on understanding the distinctive statistical properties of financial time series – (i) The probability distribution of stock price fluctuations: Stock price fluctuations occur in all magnitudes, in analogy to earthquakes – from tiny fluctuations to very drastic events, such as the crash of 19 October 1987, sometimes referred to as “Black Monday”. The distribution of price fluctuations decays with a power-law tail well outside the Lévy stable regime and describes fluctuations that differ by as much as 8 orders of magnitude. In addition, this distribution preserves its functional form for fluctuations on time scales that differ by 3 orders of magnitude, from 1 min up to approximately 10 days. (ii) Correlations in financial time series: While price fluctuations themselves have rapidly decaying correlations, the magnitude of fluctuations measured by either the absolute value or the square of the price fluctuations has correlations that decay as a power-law, persisting for several months. (iii) Volatility and trading activity: We quantify the relation between trading activity – measured by the number of transactions NΔt – and the price change GΔt for a given stock, over a time interval [t,t+Δt]. We find that NΔt displays long-range power-law correlations in time, which leads to the interpretation that the long-range correlations previously found for |GΔt| are connected to those of NΔt.

Suggested Citation

  • Gopikrishnan, P & Plerou, V & Liu, Y & Amaral, L.A.N & Gabaix, X & Stanley, H.E, 2000. "Scaling and correlation in financial time series," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 362-373.
    • Handle: RePEc:eee:phsmap:v:287:y:2000:i:3:p:362-373
    DOI: 10.1016/S0378-4371(00)00375-7
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437100003757
    Download Restriction: Full text for ScienceDirect subscribers only. Journal offers the option of making the article available online on Science direct for a fee of $3,000
    File URL: https://libkey.io/10.1016/S0378-4371(00)00375-7?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. J. Doyne Farmer, 2000. "Physicists Attempt To Scale The Ivory Towers Of Finance," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 3(03), pages 311-333.
    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. Selçuk, Faruk & Gençay, Ramazan, 2006. "Intraday dynamics of stock market returns and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 367(C), pages 375-387.
    2. C. Lawrenz & F. Westerhoff, 2003. "Modeling Exchange Rate Behavior with a Genetic Algorithm," Computational Economics, Springer;Society for Computational Economics, vol. 21(3), pages 209-229, June.
    3. Shi-Woei Lin & Hui-Lung Huang, 2007. "Agent-Based Modeling To Investigate The Disposition Effect In Financial Markets," Portuguese Journal of Management Studies, ISEG, Universidade de Lisboa, vol. 0(2), pages 145-163.
    4. J. Doyne Farmer, 2002. "Market force, ecology and evolution," Industrial and Corporate Change, Oxford University Press and the Associazione ICC, vol. 11(5), pages 895-953, November.
    5. Giardina, Irene & Bouchaud, Jean-Philippe, 2003. "Volatility clustering in agent based market models," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 6-16.
    6. Ingve Simonsen & Mogens H. Jensen & Anders Johansen, 2002. "Optimal Investment Horizons," Papers cond-mat/0202352, arXiv.org.
    7. Valdez, Emiliano A. & Dhaene, Jan & Maj, Mateusz & Vanduffel, Steven, 2009. "Bounds and approximations for sums of dependent log-elliptical random variables," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 385-397, June.
    8. Zawadowski, A.G & Karádi, R & Kertész, J, 2002. "Price drops, fluctuations, and correlation in a multi-agent model of stock markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 316(1), pages 403-412.
    9. Cross, Rod & Grinfeld, Michael & Lamba, Harbir & Seaman, Tim, 2005. "A threshold model of investor psychology," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 354(C), pages 463-478.
    10. Eisler, Z. & Kertész, J., 2004. "Multifractal model of asset returns with leverage effect," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 343(C), pages 603-622.
    11. Jean-Philippe Bouchaud, 2002. "An introduction to statistical finance," Science & Finance (CFM) working paper archive 313238, Science & Finance, Capital Fund Management.
    12. Jean-Philippe Bouchaud, 2000. "Power-laws in economics and finance: some ideas from physics," Science & Finance (CFM) working paper archive 500023, Science & Finance, Capital Fund Management.
    13. Y. Malevergne & V. F. Pisarenko & D. Sornette, 2003. "Empirical Distributions of Log-Returns: between the Stretched Exponential and the Power Law?," Papers physics/0305089, arXiv.org.
    14. Frank Schweitzer & Giorgio Fagiolo & Didier Sornette & Fernando Vega-Redondo & Douglas R. White, 2009. "Economic Networks: What Do We Know And What Do We Need To Know?," Advances in Complex Systems (ACS), World Scientific Publishing Co. Pte. Ltd., vol. 12(04n05), pages 407-422.
    15. Eduardo Zambrano, 2004. "The Interplay between Analytics and Computation in the Study of Congestion Externalities: The Case of the El Farol Problem," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 6(2), pages 375-395, May.
    16. Schinckus, Christophe, 2010. "Is econophysics a new discipline? The neopositivist argument," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(18), pages 3814-3821.
    17. Anderson, Nicola & Noss, Joseph, 2013. "Financial Stability Paper No 23: The Fractal Market Hypothesis and its implications for the stability of financial markets," Bank of England Financial Stability Papers 23, Bank of England.
    18. Fei Ren & Wei-Xing Zhou, 2014. "Dynamic Evolution of Cross-Correlations in the Chinese Stock Market," PLOS ONE, Public Library of Science, vol. 9(5), pages 1-15, May.
    19. Ferreira, Fernando F & Francisco, Gerson & Machado, Birajara S & Muruganandam, Paulsamy, 2003. "Time series analysis for minority game simulations of financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 321(3), pages 619-632.
    20. Carl Chiarella & Tony He, 2002. "An Adaptive Model on Asset Pricing and Wealth Dynamics with Heterogeneous Trading Strategies," Computing in Economics and Finance 2002 135, Society for Computational Economics.

    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:eee:phsmap:v:287:y:2000:i:3:p:362-373. 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: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/ .

    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.