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Multidimensional minimal spanning tree: The Dow Jones case

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  • Brida, Juan Gabriel
  • Risso, Wiston Adrián

Abstract

This paper introduces a new methodology in order to construct Minimal Spanning Trees (MST) and Hierarchical Trees (HT) using the information provided by more than one variable. In fact, the Symbolic Time Series Analysis (STSA) approach is applied to the Dow Jones companies using information not only from asset returns but also for trading volume. The US stock market structure is obtained, showing eight clusters of companies and General Electric as a central node in the tree. We use different partitions showing that the results do not depend on the particular partition. In addition, we apply Monte Carlo simulations suggesting that the tree is not the result of random connections.

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Bibliographic Info

Article provided by Elsevier in its journal Physica A: Statistical Mechanics and its Applications.

Volume (Year): 387 (2008)
Issue (Month): 21 ()
Pages: 5205-5210

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Handle: RePEc:eee:phsmap:v:387:y:2008:i:21:p:5205-5210

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Web page: http://www.journals.elsevier.com/physica-a-statistical-mechpplications/

Related research

Keywords: Symbolic time series analysis; Financial asset returns; Hierarchical tree;

References

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  1. Giovanni Bonanno & Fabrizio Lillo & Rosario N. Mantegna, 2001. "Levels of complexity in financial markets," Papers cond-mat/0104369, arXiv.org.
  2. R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 11(1), pages 193-197, September.
  3. Rogalski, Richard J, 1978. "The Dependence of Prices and Volume," The Review of Economics and Statistics, MIT Press, vol. 60(2), pages 268-74, May.
  4. Halinen, Aino & Törnroos, Jan-Åke, 1998. "The role of embeddedness in the evolution of business networks," Scandinavian Journal of Management, Elsevier, vol. 14(3), pages 187-205, March.
  5. Karpoff, Jonathan M., 1987. "The Relation between Price Changes and Trading Volume: A Survey," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 22(01), pages 109-126, March.
  6. Morgan, I G, 1976. "Stock Prices and Heteroscedasticity," The Journal of Business, University of Chicago Press, vol. 49(4), pages 496-508, October.
  7. Westerfield, Randolph, 1977. "The Distribution of Common Stock Price Changes: An Application of Transactions Time and Subordinated Stochastic Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(05), pages 743-765, December.
  8. G. Bonanno & G. Caldarelli & F. Lillo & S. Micciche` & N. Vandewalle & R. N. Mantegna, 2004. "Networks of equities in financial markets," Papers cond-mat/0401300, arXiv.org.
  9. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
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Citations

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Cited by:
  1. N. Garrido & F. Mureddu, 2011. "Italian economic dualism and convergence clubs at regional level," Working Paper CRENoS 201116, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  2. Leonidas Sandoval Junior, 2011. "Cluster formation and evolution in networks of financial market indices," Papers 1111.5069, arXiv.org.
  3. Lee, Junghoon & Youn, Janghyuk & Chang, Woojin, 2012. "Intraday volatility and network topological properties in the Korean stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(4), pages 1354-1360.
  4. Tabak, Benjamin M. & Serra, Thiago R. & Cajueiro, Daniel O., 2010. "Topological properties of stock market networks: The case of Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3240-3249.
  5. Papadimitriou, Theophilos & Gogas, Periklis & Tabak, Benjamin M., 2013. "Complex networks and banking systems supervision," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 392(19), pages 4429-4434.
  6. Leonidas Sandoval Junior, 2011. "Pruning a Minimum Spanning Tree," Papers 1109.0642, arXiv.org.
  7. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.
  8. Sandoval, Leonidas Junior, 2013. "To lag or not to lag? How to compare indices of stock markets that operate at different times," Insper Working Papers wpe_319, Insper Working Paper, Insper Instituto de Ensino e Pesquisa.
  9. Leonidas Sandoval Junior, 2011. "A Map of the Brazilian Stock Market," Papers 1107.4146, arXiv.org, revised Mar 2013.
  10. M. Deidda & N. Garrido & M. Pulina, 2011. "Exploring the dynamics of the efficiency in the Italian hospitality sector. A regional case study," Working Paper CRENoS 201117, Centre for North South Economic Research, University of Cagliari and Sassari, Sardinia.
  11. Cheong, Siew Ann & Fornia, Robert Paulo & Lee, Gladys Hui Ting & Kok, Jun Liang & Yim, Woei Shyr & Xu, Danny Yuan & Zhang, Yiting, 2012. "The Japanese economy in crises: A time series segmentation study," Economics - The Open-Access, Open-Assessment E-Journal, Kiel Institute for the World Economy, vol. 6(5), pages 1-81.
  12. Juan Gabriel Brida & Nicolás Garrido & Silvia London, 2011. "Estudio del Desempeño Económico Regional: el caso Argentino," Documentos de Trabajo en Economia y Ciencia Regional 12, Universidad Catolica del Norte, Chile, Department of Economics, revised May 2011.
  13. 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.
  14. Sandoval, Leonidas & Franca, Italo De Paula, 2012. "Correlation of financial markets in times of crisis," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(1), pages 187-208.
  15. Sandoval, Leonidas, 2012. "Pruning a minimum spanning tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2678-2711.
  16. Sandoval, Leonidas, 2014. "To lag or not to lag? How to compare indices of stock markets that operate on different times," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 403(C), pages 227-243.

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