IDEAS home Printed from https://ideas.repec.org/p/arx/papers/1109.0642.html
   My bibliography  Save this paper

Pruning a Minimum Spanning Tree

Author

Listed:
  • Leonidas Sandoval Junior

Abstract

This work employs some techniques in order to filter random noise from the information provided by minimum spanning trees obtained from the correlation matrices of international stock market indices prior to and during times of crisis. The first technique establishes a threshold above which connections are considered affected by noise, based on the study of random networks with the same probability density distribution of the original data. The second technique is to judge the strengh of a connection by its survival rate, which is the amount of time a connection between two stock market indices endure. The idea is that true connections will survive for longer periods of time, and that random connections will not. That information is then combined with the information obtained from the first technique in order to create a smaller network, where most of the connections are either strong or enduring in time.

Suggested Citation

  • Leonidas Sandoval Junior, 2011. "Pruning a Minimum Spanning Tree," Papers 1109.0642, arXiv.org.
  • Handle: RePEc:arx:papers:1109.0642
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/1109.0642
    File Function: Latest version
    Download Restriction: no

    References listed on IDEAS

    as
    1. Giorgio Fagiolo, 2010. "The international-trade network: gravity equations and topological properties," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 5(1), pages 1-25, June.
    2. Reginald D. Smith, 2009. "The Spread of the Credit Crisis: View from a Stock Correlation Network," Papers 0901.1392, arXiv.org, revised Jun 2009.
    3. G. Bonanno & F. Lillo & R. N. Mantegna, 2001. "High-frequency cross-correlation in a set of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 96-104.
    4. Stefania Vitali & James B. Glattfelder & Stefano Battiston, 2011. "The network of global corporate control," Papers 1107.5728, arXiv.org, revised Sep 2011.
    5. Rudi Schafer & Markus Sjolin & Andreas Sundin & Michal Wolanski & Thomas Guhr, 2007. "Credit risk - A structural model with jumps and correlations," Papers 0707.3478, arXiv.org, revised Jul 2007.
    6. Onnela, J.-P. & Chakraborti, A. & Kaski, K. & Kertész, J., 2003. "Dynamic asset trees and Black Monday," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 247-252.
    7. Pawe{l} Sieczka & Janusz A. Ho{l}yst, 2008. "Correlations in commodity markets," Papers 0803.3884, arXiv.org, revised Jan 2009.
    8. Rigobon, Roberto, 2003. "On the measurement of the international propagation of shocks: is the transmission stable?," Journal of International Economics, Elsevier, vol. 61(2), pages 261-283, December.
    9. Coelho, Ricardo & Gilmore, Claire G. & Lucey, Brian & Richmond, Peter & Hutzler, Stefan, 2007. "The evolution of interdependence in world equity markets—Evidence from minimum spanning trees," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 376(C), pages 455-466.
    10. Dong-Ming Song & Michele Tumminello & Wei-Xing Zhou & Rosario N. Mantegna, 2011. "Evolution of worldwide stock markets, correlation structure and correlation based graphs," Papers 1103.5555, arXiv.org.
    11. Miccichè, Salvatore & Bonanno, Giovanni & Lillo, Fabrizio & N. Mantegna, Rosario, 2003. "Degree stability of a minimum spanning tree of price return and volatility," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 324(1), pages 66-73.
    12. Gai, Prasanna & Kapadia, Sujit, 2010. "Contagion in financial networks," Bank of England working papers 383, Bank of England.
    13. Luca De Benedictis & Lucia Tajoli, 2011. "The World Trade Network," The World Economy, Wiley Blackwell, vol. 34(8), pages 1417-1454, August.
    14. Brida, Juan Gabriel & Risso, Wiston Adrián, 2008. "Multidimensional minimal spanning tree: The Dow Jones case," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 387(21), pages 5205-5210.
    15. Sitabhra Sinha & Raj Kumar Pan, 2007. "Uncovering the Internal Structure of the Indian Financial Market: Cross-correlation behavior in the NSE," Papers 0704.2115, arXiv.org.
    16. Ausloos, M. & Lambiotte, R., 2007. "Clusters or networks of economies? A macroeconomy study through Gross Domestic Product," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 16-21.
    17. Keskin, Mustafa & Deviren, Bayram & Kocakaplan, Yusuf, 2011. "Topology of the correlation networks among major currencies using hierarchical structure methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(4), pages 719-730.
    18. Michel Beine & Gunther Capelle-Blancard & Helene Raymond, 2008. "International nonlinear causality between stock markets," The European Journal of Finance, Taylor & Francis Journals, vol. 14(8), pages 663-686.
    19. Bessler, David A. & Yang, Jian, 2003. "The structure of interdependence in international stock markets," Journal of International Money and Finance, Elsevier, vol. 22(2), pages 261-287, April.
    20. Jiankui He & Michael W. Deem, 2010. "Structure and Response in the World Trade Network," Papers 1010.0410, arXiv.org.
    21. Dror Y. Kenett & Yoash Shapira & Asaf Madi & Sharron Bransburg-Zabary & Gitit Gur-Gershgoren & Eshel Ben-Jacob, 2010. "Dynamics of Stock Market Correlations," Czech Economic Review, Charles University Prague, Faculty of Social Sciences, Institute of Economic Studies, vol. 4(3), pages 330-340, November.
    22. Cheong, Siew Ann & Fornia, Robert Paulo & Lee, Gladys Hui Ting & Kok, Jun Liang & Yim, Woei Shyr & Xu, Danny Yuan & Zhang, Yiting, 2011. "The Japanese economy in crises: A time series segmentation study," Economics Discussion Papers 2011-24, Kiel Institute for the World Economy (IfW).
    23. Kyu-Min Lee & Jae-Suk Yang & Gunn Kim & Jaesung Lee & Kwang-Il Goh & In-mook Kim, 2010. "Impact of the topology of global macroeconomic network on the spreading of economic crises," Papers 1011.4336, arXiv.org, revised Apr 2011.
    24. Jaroslaw Kwapien & Sylwia Gworek & Stanislaw Drozdz, 2009. "Structure and evolution of the foreign exchange networks," Papers 0901.4793, arXiv.org.
    25. Naylor, Michael J. & Rose, Lawrence C. & Moyle, Brendan J., 2007. "Topology of foreign exchange markets using hierarchical structure methods," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 382(1), pages 199-208.
    26. Jarosław Kwapień & Sylwia Gworek & Stanisław Drożdż & Andrzej Górski, 2009. "Analysis of a network structure of the foreign currency exchange market," Journal of Economic Interaction and Coordination, Springer;Society for Economic Science with Heterogeneous Interacting Agents, vol. 4(1), pages 55-72, June.
    27. Yiting Zhang & Gladys Hui Ting Lee & Jian Cheng Wong & Jun Liang Kok & Manamohan Prusty & Siew Ann Cheong, 2010. "Will the US Economy Recover in 2010? A Minimal Spanning Tree Study," Papers 1009.5800, arXiv.org, revised Dec 2010.
    28. Sieczka, Paweł & Hołyst, Janusz A., 2009. "Correlations in commodity markets," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(8), pages 1621-1630.
    29. Jaroslaw Kwapien & Sylwia Gworek & Stanislaw Drozdz & Andrzej Gorski, 2009. "Analysis of a network structure of the foreign currency exchange market," Papers 0906.0480, arXiv.org.
    30. N. Lesca, 2010. "Introduction," Post-Print halshs-00640602, HAL.
    Full references (including those not matched with items on IDEAS)

    More about this item

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:arx:papers:1109.0642. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (arXiv administrators). General contact details of provider: http://arxiv.org/ .

    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 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.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.