IDEAS home Printed from https://ideas.repec.org/a/spr/eurphb/v71y2009i4p511-522.html

Empirical behavior of a world stock index from intra-day to monthly time scales

Author

Listed:
  • W. Breymann
  • D. R. Lüthi

  • E. Platen

Abstract

Most of the papers that study the distributional and fractal properties of financial instruments focus on stock prices or foreign exchange rates. This typically leads to mixed results concerning the distributions of log-returns and some multi-fractal properties of exchange rates, stock prices, and regional indices. This paper uses a well diversified world stock index as the central object of analysis. Such index approximates the growth optimal portfolio, which is demonstrated under the benchmark approach, it is the ideal reference unit for studying basic securities. When denominating this world index in units of a given currency, one measures the movements of the currency against the entire market. This provides a least disturbed observation of the currency dynamics. In this manner, one can expect to disentangle, e.g., the superposition of the two currencies involved in an exchange rate. This benchmark approach to the empirical analysis of financial data allows us to establish remarkable stylized facts. Most important is the observation that the repeatedly documented multi-fractal appearance of financial time series is very weak and much less pronounced than the deviation of the mono-scaling properties from Brownian-motion type scaling. The generalized Hurst exponent H(2) assumes typical values between 0.55 and 0.6. Accordingly, autocorrelations of log-returns decay according to a power law, and the quadratic variation vanishes when going to vanishing observation time step size. Furthermore, one can identify the Student t distribution as the log-return distribution of a well-diversified world stock index for long time horizons when a long enough data series is used for estimation. The study of dependence properties, finally, reveals that jumps at daily horizon originate primarily in the stock market while at 5 min horizon they originate in the foreign exchange market. These results are contrasted with the behavior of foreign exchange rates. The principal message of
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • W. Breymann & D. R. Lüthi & E. Platen, 2009. "Empirical behavior of a world stock index from intra-day to monthly time scales," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 71(4), pages 511-522, October.
    • Handle: RePEc:spr:eurphb:v:71:y:2009:i:4:p:511-522
    DOI: 10.1140/epjb/e2009-00341-x
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1140/epjb/e2009-00341-x
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1140/epjb/e2009-00341-x?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 look for a different version below or

    for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    2. Gençay, Ramazan & Dacorogna, Michel & Muller, Ulrich A. & Pictet, Olivier & Olsen, Richard, 2001. "An Introduction to High-Frequency Finance," Elsevier Monographs, Elsevier, edition 1, number 9780122796715.
    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. Eckhard Platen, 2026. "Information-Theoretic Approach to Financial Market Modelling," Papers 2602.14575, arXiv.org.
    2. William T. Shaw, 2011. "Risk, VaR, CVaR and their associated Portfolio Optimizations when Asset Returns have a Multivariate Student T Distribution," Papers 1102.5665, arXiv.org.
    3. Eckhard Platen, 2025. "Information-minimizing stationary financial market dynamics," Papers 2507.18395, arXiv.org.
    4. Mansooreh Kazemilari & Maman Abdurachman Djauhari & Zuhaimy Ismail, 2016. "Foreign Exchange Market Performance: Evidence from Bivariate Time Series Approach," Papers 1608.07694, arXiv.org.

    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. Platen, Eckhard, 2006. "Portfolio selection and asset pricing under a benchmark approach," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 370(1), pages 23-29.
    2. Detlef Seese & Christof Weinhardt & Frank Schlottmann (ed.), 2008. "Handbook on Information Technology in Finance," International Handbooks on Information Systems, Springer, number 978-3-540-49487-4, June.
    3. Dash, Saumya Ranjan & Maitra, Debasish, 2018. "Does sentiment matter for stock returns? Evidence from Indian stock market using wavelet approach," Finance Research Letters, Elsevier, vol. 26(C), pages 32-39.
    4. Lallouache, Mehdi & Abergel, Frédéric, 2014. "Tick size reduction and price clustering in a FX order book," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 416(C), pages 488-498.
    5. Dufour, Jean-Marie & García, René & Taamouti, Abderrahim, 2008. "Measuring causality between volatility and returns with high-frequency data," UC3M Working papers. Economics we084422, Universidad Carlos III de Madrid. Departamento de Economía.
    6. Kaijian He & Rui Zha & Jun Wu & Kin Keung Lai, 2016. "Multivariate EMD-Based Modeling and Forecasting of Crude Oil Price," Sustainability, MDPI, vol. 8(4), pages 1-11, April.
    7. Ozcan Ceylan, 2015. "Limited information-processing capacity and asymmetric stock correlations," Quantitative Finance, Taylor & Francis Journals, vol. 15(6), pages 1031-1039, June.
    8. Nour Meddahi, 2002. "A theoretical comparison between integrated and realized volatility," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 17(5), pages 479-508.
    9. Nicola Bruti-Liberati & Christina Nikitopoulos-Sklibosios & Eckhard Platen & Erik Schlögl, 2009. "Alternative Defaultable Term Structure Models," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(1), pages 1-31, March.
    10. Monira Essa Aloud, 2016. "Time Series Analysis Indicators under Directional Changes: The Case of Saudi Stock Market," International Journal of Economics and Financial Issues, Econjournals, vol. 6(1), pages 55-64.
    11. Vassilios G. Papavassiliou, 2016. "Allowing For Jump Measurements In Volatility: A High-Frequency Financial Data Analysis Of Individual Stocks," Bulletin of Economic Research, Wiley Blackwell, vol. 68(2), pages 124-132, April.
    12. Monira Essa Aloud, 2016. "Profitability of Directional Change Based Trading Strategies: The Case of Saudi Stock Market," International Journal of Economics and Financial Issues, Econjournals, vol. 6(1), pages 87-95.
    13. Dean Buckner & Kevin Dowd & Hardy Hulley, 2024. "Arbitrage problems with reflected geometric Brownian motion," Finance and Stochastics, Springer, vol. 28(1), pages 1-26, January.
    14. Kevin Fergusson & Eckhard Platen, 2006. "On the Distributional Characterization of Daily Log-Returns of a World Stock Index," Applied Mathematical Finance, Taylor & Francis Journals, vol. 13(1), pages 19-38.
    15. Vladimir Cherny & Jan Obłój, 2013. "Portfolio optimisation under non-linear drawdown constraints in a semimartingale financial model," Finance and Stochastics, Springer, vol. 17(4), pages 771-800, October.
    16. 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.
    17. Stefanescu, Razvan & Dumitriu, Ramona, 2015. "Conţinutul analizei seriilor de timp financiare [The Essentials of the Analysis of Financial Time Series]," MPRA Paper 67175, University Library of Munich, Germany.
    18. Feng, Yuanhua, 2002. "Modelling Different Volatility Components," CoFE Discussion Papers 02/18, University of Konstanz, Center of Finance and Econometrics (CoFE).
    19. Caporin, Massimiliano & Chang, Chia-Lin & McAleer, Michael, 2019. "Are the S&P 500 index and crude oil, natural gas and ethanol futures related for intra-day data?," International Review of Economics & Finance, Elsevier, vol. 59(C), pages 50-70.
    20. repec:uts:finphd:40 is not listed on IDEAS
    21. Gencay, Ramazan & Selcuk, Faruk & Ulugulyagci, Abdurrahman, 2003. "High volatility, thick tails and extreme value theory in value-at-risk estimation," Insurance: Mathematics and Economics, Elsevier, vol. 33(2), pages 337-356, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    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:spr:eurphb:v:71:y:2009:i:4:p:511-522. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.