IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v82y2012i11p1986-1989.html

Estimating multivariate heavy tails and principal directions easily, with an application to international exchange rates

Author

Listed:
  • Tsionas, Efthymios G.

Abstract

In this paper, we consider the estimation of the tail indices of distributions in the domain of attraction of stable laws. We follow the approach of Meerschaert and Scheffler (1999), which requires exclusively the spectral decomposition of the uncentered sample moment matrix containing the moments of a collection of time series. The technique is applied successfully to ten major currencies, using daily data over the period 1996–2012.

Suggested Citation

  • Tsionas, Efthymios G., 2012. "Estimating multivariate heavy tails and principal directions easily, with an application to international exchange rates," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 1986-1989.
    • Handle: RePEc:eee:stapro:v:82:y:2012:i:11:p:1986-1989
    DOI: 10.1016/j.spl.2012.06.030
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715212002647
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2012.06.030?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

    for a different version of it.

    References listed on IDEAS

    as
    1. Loretan, Mico & Phillips, Peter C. B., 1994. "Testing the covariance stationarity of heavy-tailed time series: An overview of the theory with applications to several financial datasets," Journal of Empirical Finance, Elsevier, vol. 1(2), pages 211-248, January.
    2. Meerschaert, Mark M. & Scheffler, Hans-Peter, 1999. "Moment Estimator for Random Vectors with Heavy Tails," Journal of Multivariate Analysis, Elsevier, vol. 71(1), pages 145-159, October.
    3. McCulloch, J Huston, 1997. "Measuring Tail Thickness to Estimate the Stable Index Alpha: A Critique," Journal of Business & Economic Statistics, American Statistical Association, vol. 15(1), pages 74-81, January.
    4. B. N. Cheng & S. T. Rachev, 1995. "Multivariate Stable Futures Prices," Mathematical Finance, Wiley Blackwell, vol. 5(2), pages 133-153, April.
    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. Jensen DR, 2017. "Limits and Inferences for Alpha–Stable Variables," Biostatistics and Biometrics Open Access Journal, Juniper Publishers Inc., vol. 4(1), pages 15-18, December.

    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. Runde, Ralf & Scheffner, Axel, 1998. "On the existence of moments: With an application to German stock returns," Technical Reports 1998,25, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    2. Xiufeng Yan, 2021. "Autoregressive conditional duration modelling of high frequency data," Papers 2111.02300, arXiv.org.
    3. Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Scholarly Articles 2624460, Harvard University Department of Economics.
    4. Tsionas, Mike, 2012. "Simple techniques for likelihood analysis of univariate and multivariate stable distributions: with extensions to multivariate stochastic volatility and dynamic factor models," MPRA Paper 40966, University Library of Munich, Germany, revised 20 Aug 2012.
    5. Salhi, Khaled & Deaconu, Madalina & Lejay, Antoine & Champagnat, Nicolas & Navet, Nicolas, 2016. "Regime switching model for financial data: Empirical risk analysis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 148-157.
    6. Rustam Ibragimov & Johan Walden, 2011. "Value at risk and efficiency under dependence and heavy-tailedness: models with common shocks," Annals of Finance, Springer, vol. 7(3), pages 285-318, August.
    7. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2002. "Stationarity of stable power-GARCH processes," Journal of Econometrics, Elsevier, vol. 106(1), pages 97-107, January.
    8. Ibragimov, Rustam, 2014. "On the robustness of location estimators in models of firm growth under heavy-tailedness," Journal of Econometrics, Elsevier, vol. 181(1), pages 25-33.
    9. Mittnik, Stefan & Paolella, Marc S. & Rachev, Svetlozar T., 2000. "Diagnosing and treating the fat tails in financial returns data," Journal of Empirical Finance, Elsevier, vol. 7(3-4), pages 389-416, November.
    10. Ibragimov, Rustam & Walden, Johan, 2008. "Portfolio diversification under local and moderate deviations from power laws," Insurance: Mathematics and Economics, Elsevier, vol. 42(2), pages 594-599, April.
    11. Kurz-Kim, Jeong-Ryeol & Loretan, Mico, 2014. "On the properties of the coefficient of determination in regression models with infinite variance variables," Journal of Econometrics, Elsevier, vol. 181(1), pages 15-24.
    12. Tsionas, Mike G., 2016. "Bayesian analysis of multivariate stable distributions using one-dimensional projections," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 185-193.
    13. Ibragimov, Rustam & Walden, Johan, 2007. "The limits of diversification when losses may be large," Journal of Banking & Finance, Elsevier, vol. 31(8), pages 2551-2569, August.
    14. Ibragimov, Rustam & Prokhorov, Artem, 2016. "Heavy tails and copulas: Limits of diversification revisited," Economics Letters, Elsevier, vol. 149(C), pages 102-107.
    15. Rustam Ibragimov, 2005. "Portfolio Diversification and Value At Risk Under Thick-Tailedness," Yale School of Management Working Papers amz2386, Yale School of Management, revised 01 Aug 2005.
    16. Dongweí Su, 2003. "Risk, Return and Regulation in Chinese Stock Markets," World Scientific Book Chapters, in: Chinese Stock Markets A Research Handbook, chapter 3, pages 75-122, World Scientific Publishing Co. Pte. Ltd..
    17. Chen, Zhimin & Ibragimov, Rustam, 2019. "One country, two systems? The heavy-tailedness of Chinese A- and H- share markets," Emerging Markets Review, Elsevier, vol. 38(C), pages 115-141.
    18. Zhiguang Wang & Prasad Bidarkota, 2012. "Risk premia in forward foreign exchange rates: a comparison of signal extraction and regression methods," Empirical Economics, Springer, vol. 42(1), pages 21-51, February.
    19. Giorgio Fagiolo & Mauro Napoletano & Andrea Roventini, 2008. "Are output growth-rate distributions fat-tailed? some evidence from OECD countries," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 23(5), pages 639-669.
    20. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.

    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:eee:stapro:v:82:y:2012:i:11:p:1986-1989. 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.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    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.