IDEAS home Printed from https://ideas.repec.org/a/eee/phsmap/v269y1999i1p98-110.html
   My bibliography  Save this article

Characteristic times in stock market indices

Author

Listed:
  • Kullmann, L
  • Töyli, J
  • Kertesz, J
  • Kanto, A
  • Kaski, K

Abstract

In this study we analyze the Standard and Poor's 500 index data of the New York Stock Exchange for more than 32 years. Using a simple random walk model we demonstrate that the proper variable to look at is the logarithmic return. In the statistical analysis we have done fittings to the Lévy distribution using either the index data as such or pre-processing it with ARCH, GARCH or IGARCH methods, which tend to remove the time-dependent variance. For short times the truncated Lévy distribution is found to fit the data quite well. Since this is not a stable distribution, the scaling behavior observed for short times should brake down for longer times. We demonstrate that the characteristic time where this cross-over starts is of the order of one day.

Suggested Citation

  • Kullmann, L & Töyli, J & Kertesz, J & Kanto, A & Kaski, K, 1999. "Characteristic times in stock market indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 269(1), pages 98-110.
    • Handle: RePEc:eee:phsmap:v:269:y:1999:i:1:p:98-110
    DOI: 10.1016/S0378-4371(99)00084-9
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378437199000849
    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(99)00084-9?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. Kon, Stanley J, 1984. "Models of Stock Returns-A Comparison," Journal of Finance, American Finance Association, vol. 39(1), pages 147-165, March.
    2. M. F. M. Osborne, 1959. "Brownian Motion in the Stock Market," Operations Research, INFORMS, vol. 7(2), pages 145-173, April.
    3. Blattberg, Robert C & Gonedes, Nicholas J, 1974. "A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices," The Journal of Business, University of Chicago Press, vol. 47(2), pages 244-280, April.
    4. Schwert, G William, 1989. " Why Does Stock Market Volatility Change over Time?," Journal of Finance, American Finance Association, vol. 44(5), pages 1115-1153, December.
    5. Bollerslev, Tim, 1986. "Generalized autoregressive conditional heteroskedasticity," Journal of Econometrics, Elsevier, vol. 31(3), pages 307-327, April.
    6. Hagerman, Robert L, 1978. "More Evidence on the Distribution of Security Returns," Journal of Finance, American Finance Association, vol. 33(4), pages 1213-1221, September.
    7. Perry, Philip R., 1983. "More Evidence on the Nature of the Distribution of Security Returns," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 18(2), pages 211-221, June.
    8. Engle, Robert F, 1982. "Autoregressive Conditional Heteroscedasticity with Estimates of the Variance of United Kingdom Inflation," Econometrica, Econometric Society, vol. 50(4), pages 987-1007, July.
    9. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-547, August.
    10. Benoit Mandelbrot, 2015. "The Variation of Certain Speculative Prices," World Scientific Book Chapters, in: Anastasios G Malliaris & William T Ziemba (ed.), THE WORLD SCIENTIFIC HANDBOOK OF FUTURES MARKETS, chapter 3, pages 39-78, World Scientific Publishing Co. Pte. Ltd..
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Molina-Muñoz, Jesús & Mora-Valencia, Andrés & Perote, Javier, 2020. "Market-crash forecasting based on the dynamics of the alpha-stable distribution," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 557(C).
    2. Mark Paddrik & Roy Hayes & William Scherer & Peter Beling, 2017. "Effects of limit order book information level on market stability metrics," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 12(2), pages 221-247, July.
    3. Ivan Jericevich & Patrick Chang & Tim Gebbie, 2021. "Simulation and estimation of an agent-based market-model with a matching engine," Papers 2108.07806, arXiv.org, revised Aug 2021.
    4. Esteban Guevara Hidalgo, 2015. "Bin Size Independence in Intra-day Seasonalities for Relative Prices," Papers 1501.05176, arXiv.org, revised Dec 2016.
    5. De Domenico, Federica & Livan, Giacomo & Montagna, Guido & Nicrosini, Oreste, 2023. "Modeling and simulation of financial returns under non-Gaussian distributions," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 622(C).
    6. Guevara Hidalgo, Esteban, 2017. "Bin size independence in intra-day seasonalities for relative prices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 468(C), pages 722-732.
    7. Gillemot, L. & Töyli, J. & Kertesz, J. & Kaski, K., 2000. "Time-independent models of asset returns revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 304-324.
    8. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: II. Agent-based models," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 1013-1041.
    9. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frédéric Abergel, 2011. "Econophysics review: I. Empirical facts," Post-Print hal-00621058, HAL.
    10. Anirban Chakraborti & Ioane Muni Toke & Marco Patriarca & Frederic Abergel, 2011. "Econophysics review: I. Empirical facts," Quantitative Finance, Taylor & Francis Journals, vol. 11(7), pages 991-1012.
    11. 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.
    12. Janecskó, Balázs, 2000. "Idősor-modellezés és opcióárazás csonkolt Lévy-eloszlással [Time-series modelling and option pricing with a truncated Lévy distribution]," Közgazdasági Szemle (Economic Review - monthly of the Hungarian Academy of Sciences), Közgazdasági Szemle Alapítvány (Economic Review Foundation), vol. 0(11), pages 899-917.
    13. Zhang, Yiting & Lee, Gladys Hui Ting & Wong, Jian Cheng & Kok, Jun Liang & Prusty, Manamohan & Cheong, Siew Ann, 2011. "Will the US economy recover in 2010? A minimal spanning tree study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2020-2050.
    14. López Martín, María del Mar & García, Catalina García & García Pérez, José, 2012. "Treatment of kurtosis in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2032-2045.

    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. Gillemot, L. & Töyli, J. & Kertesz, J. & Kaski, K., 2000. "Time-independent models of asset returns revisited," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 282(1), pages 304-324.
    2. David Edelman & Thomas Gillespie, 2000. "The Stochastically Subordinated Poisson Normal Process for Modelling Financial Assets," Annals of Operations Research, Springer, vol. 100(1), pages 133-164, December.
    3. Phoebe Koundouri & Nikolaos Kourogenis & Nikitas Pittis, 2016. "Statistical Modeling Of Stock Returns: Explanatory Or Descriptive? A Historical Survey With Some Methodological Reflections," Journal of Economic Surveys, Wiley Blackwell, vol. 30(1), pages 149-164, February.
    4. Eom, Cheoljun & Kaizoji, Taisei & Scalas, Enrico, 2019. "Fat tails in financial return distributions revisited: Evidence from the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 526(C).
    5. Kim, Dongcheol & Kon, Stanley J., 1999. "Structural change and time dependence in models of stock returns," Journal of Empirical Finance, Elsevier, vol. 6(3), pages 283-308, September.
    6. Degiannakis, Stavros & Xekalaki, Evdokia, 2004. "Autoregressive Conditional Heteroskedasticity (ARCH) Models: A Review," MPRA Paper 80487, University Library of Munich, Germany.
    7. Bollerslev, Tim & Engle, Robert F. & Nelson, Daniel B., 1986. "Arch models," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 49, pages 2959-3038, Elsevier.
    8. López Martín, María del Mar & García, Catalina García & García Pérez, José, 2012. "Treatment of kurtosis in financial markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(5), pages 2032-2045.
    9. Wai Mun Fong, 1997. "Robust beta estimation: Some empirical evidence," Review of Financial Economics, John Wiley & Sons, vol. 6(2), pages 167-186.
    10. Fong, Wai Mun, 1997. "Robust beta estimation: Some empirical evidence," Review of Financial Economics, Elsevier, vol. 6(2), pages 167-186.
    11. Maria S. Heracleous, 2007. "Sample Kurtosis, GARCH-t and the Degrees of Freedom Issue," Economics Working Papers ECO2007/60, European University Institute.
    12. Mondher Bellalah & Marc Lavielle, 2002. "A Decomposition of Empirical Distributions with Applications to the Valuation of Derivative Assets," Multinational Finance Journal, Multinational Finance Journal, vol. 6(2), pages 99-130, June.
    13. Debabrata Mukhopadhyay & Nityananda Sarkar, 2013. "Stock Returns Under Alternative Volatility and Distributional Assumptions: The Case for India," International Econometric Review (IER), Econometric Research Association, vol. 5(1), pages 1-19, April.
    14. de Vries, Casper G., 1991. "On the relation between GARCH and stable processes," Journal of Econometrics, Elsevier, vol. 48(3), pages 313-324, June.
    15. Stefan Mittnik & Marc Paolella & Svetlozar Rachev, 1998. "Unconditional and Conditional Distributional Models for the Nikkei Index," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 5(2), pages 99-128, May.
    16. BAUWENS, Luc & HAFNER, Christian & LAURENT, Sébastien, 2011. "Volatility models," LIDAM Discussion Papers CORE 2011058, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
      • Bauwens, L. & Hafner, C. & Laurent, S., 2012. "Volatility Models," LIDAM Reprints ISBA 2012028, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
      • Bauwens, L. & Hafner C. & Laurent, S., 2011. "Volatility Models," LIDAM Discussion Papers ISBA 2011044, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    17. Xu, Cheng Kenneth, 2000. "The microstructure of the Chinese stock market," China Economic Review, Elsevier, vol. 11(1), pages 79-97.
    18. MEDDAHI, Nour, 2001. "An Eigenfunction Approach for Volatility Modeling," Cahiers de recherche 2001-29, Universite de Montreal, Departement de sciences economiques.
    19. Dinghai Xu & Tony S. Wirjanto, 2008. "An Empirical Characteristic Function Approach to VaR under a Mixture of Normal Distribution with Time-Varying Volatility," Working Papers 08008, University of Waterloo, Department of Economics.
    20. Hentschel, Ludger, 1995. "All in the family Nesting symmetric and asymmetric GARCH models," Journal of Financial Economics, Elsevier, vol. 39(1), pages 71-104, September.

    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:eee:phsmap:v:269:y:1999:i:1:p:98-110. 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.