IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v140y2015icp317-324.html
   My bibliography  Save this article

Entropy measure for the quantification of upper quantile interdependence in multivariate distributions

Author

Listed:
  • Rodríguez, Jhan
  • Bárdossy, András

Abstract

We study the applicability of a measure of interdependence among the components of a random vector along the main diagonal of the vector’s copula, i.e. along the line u1=⋯=uJ, for (u1,…,uJ)∈[0,1]J. Our measure is related to the Shannon entropy of a discrete random variable, and it is a measure of local divergence between the data empirical copula and the independent copula. Hence we call it a “local dependence entropy index”, which can be interpreted as an effective number of independent variables. It is invariant with respect to marginal non-decreasing transformations and can be used in arbitrary dimensions. We show the applicability of our entropy index by an example with real data of 4 stock prices of the DAX index. In case the random vector possesses an extreme value copula, the index is shown to have as limit the extremal coefficient, which can be interpreted as the effective number of asymptotically independent components in the vector.

Suggested Citation

  • Rodríguez, Jhan & Bárdossy, András, 2015. "Entropy measure for the quantification of upper quantile interdependence in multivariate distributions," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 317-324.
    • Handle: RePEc:eee:jmvana:v:140:y:2015:i:c:p:317-324
    DOI: 10.1016/j.jmva.2015.05.004
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047259X15001190
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.jmva.2015.05.004?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. Abberger, Klaus, 2004. "A simple graphical method to explore tail-dependence in stock-return pairs," CoFE Discussion Papers 04/03, University of Konstanz, Center of Finance and Econometrics (CoFE).
    2. Micheas, Athanasios C. & Zografos, Konstantinos, 2006. "Measuring stochastic dependence using [phi]-divergence," Journal of Multivariate Analysis, Elsevier, vol. 97(3), pages 765-784, March.
    3. Martin Schlather, 2003. "A dependence measure for multivariate and spatial extreme values: Properties and inference," Biometrika, Biometrika Trust, vol. 90(1), pages 139-156, March.
    4. Dhaene, Jan & Linders, Daniël & Schoutens, Wim & Vyncke, David, 2012. "The Herd Behavior Index: A new measure for the implied degree of co-movement in stock markets," Insurance: Mathematics and Economics, Elsevier, vol. 50(3), pages 357-370.
    5. Fisher N. I. & Switzer P., 2001. "Graphical Assessment of Dependence: Is a Picture Worth 100 Tests?," The American Statistician, American Statistical Association, vol. 55, pages 233-239, August.
    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. Mohamed Es-Sanoun & Jude Gohou & Mounir Benboubker, 2023. "Testing of Herd Behavior In african Stock Markets During COVID-19 Pandemic [Essai de vérification du comportement mimétique dans les marchés boursiers africains au cours de la crise de covid-19]," Post-Print hal-04144289, HAL.
    2. Park, Beum-Jo & Kim, Myung-Joong, 2017. "A Dynamic Measure of Intentional Herd Behavior in Financial Markets," MPRA Paper 82025, University Library of Munich, Germany.
    3. Puput Tri Komalasari & Marwan Asri & Bernardinus M. Purwanto & Bowo Setiyono, 2022. "Herding behaviour in the capital market: What do we know and what is next?," Management Review Quarterly, Springer, vol. 72(3), pages 745-787, September.
    4. Sebastian Engelke & Stanislav Volgushev, 2022. "Structure learning for extremal tree models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 84(5), pages 2055-2087, November.
    5. Karl Siburg & Pavel Stoimenov, 2010. "A measure of mutual complete dependence," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 71(2), pages 239-251, March.
    6. Daniël Linders & Jan Dhaene & Wim Schoutens, 2015. "Option prices and model-free measurement of implied herd behavior in stock markets," International Journal of Financial Engineering (IJFE), World Scientific Publishing Co. Pte. Ltd., vol. 2(02), pages 1-35.
    7. Mhalla, Linda & Chavez-Demoulin, Valérie & Naveau, Philippe, 2017. "Non-linear models for extremal dependence," Journal of Multivariate Analysis, Elsevier, vol. 159(C), pages 49-66.
    8. Cheung, Ka Chun & Lo, Ambrose, 2013. "General lower bounds on convex functionals of aggregate sums," Insurance: Mathematics and Economics, Elsevier, vol. 53(3), pages 884-896.
    9. Abberger, Klaus, 2004. "A simple graphical method to explore tail-dependence in stock-return pairs," CoFE Discussion Papers 04/03, University of Konstanz, Center of Finance and Econometrics (CoFE).
    10. Einmahl, John & Kiriliouk, Anna & Segers, Johan, 2016. "A continuous updating weighted least squares estimator of tail dependence in high dimensions," LIDAM Discussion Papers ISBA 2016002, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    11. Nguyen, Cuong & Ishaq Bhatti, M. & Henry, Darren, 2017. "Are Vietnam and Chinese stock markets out of the US contagion effect in extreme events?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 480(C), pages 10-21.
    12. Apratim Guha & Atanu Biswas & Abhik Ghosh, 2021. "A nonparametric two‐sample test using a general φ‐divergence‐based mutual information," Statistica Neerlandica, Netherlands Society for Statistics and Operations Research, vol. 75(2), pages 180-202, May.
    13. Papastathopoulos, Ioannis & Tawn, Jonathan A., 2014. "Dependence properties of multivariate max-stable distributions," Journal of Multivariate Analysis, Elsevier, vol. 130(C), pages 134-140.
    14. Canela Miguel-Angel & Pedreira Eduardo, 2012. "Modelling Dependence in Latin American Markets Using Copula Functions," Journal of Emerging Market Finance, Institute for Financial Management and Research, vol. 11(3), pages 231-270, December.
    15. M. Mehdi Bateni & Mario L. V. Martina & ·Marcello Arosio, 2022. "Multivariate return period for different types of flooding in city of Monza, Italy," Natural Hazards: Journal of the International Society for the Prevention and Mitigation of Natural Hazards, Springer;International Society for the Prevention and Mitigation of Natural Hazards, vol. 114(1), pages 811-823, October.
    16. Tan, Sook-Rei & Li, Changtai & Yeap, Xiu Wei, 2022. "A time-varying copula approach for constructing a daily financial systemic stress index," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    17. Brunella Bonaccorso & Giuseppe T. Aronica, 2016. "Estimating Temporal Changes in Extreme Rainfall in Sicily Region (Italy)," Water Resources Management: An International Journal, Published for the European Water Resources Association (EWRA), Springer;European Water Resources Association (EWRA), vol. 30(15), pages 5651-5670, December.
    18. Padoan, Simone A., 2011. "Multivariate extreme models based on underlying skew-t and skew-normal distributions," Journal of Multivariate Analysis, Elsevier, vol. 102(5), pages 977-991, May.
    19. Erwan Koch, 2019. "Spatial Risk Measures and Rate of Spatial Diversification," Risks, MDPI, vol. 7(2), pages 1-26, May.
    20. Bracalente, Bruno & Polinori, Paolo, 2010. "L’efficienza tecnico-economica dei servizi pubblici locali: i casi delle farmacie comunali e dei servizi di igiene urbana [Technical And Economic Efficiency Of Local Public Services: The Cases Of T," MPRA Paper 34455, University Library of Munich, Germany.

    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:jmvana:v:140:y:2015:i:c:p:317-324. 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.