IDEAS home Printed from https://ideas.repec.org/a/ibf/riafin/v6y2013i6p15-28.html
   My bibliography  Save this article

Spectral Analysis And Networks In Financial Correlation Matrices, Analisis Espectral Y Redes En Matrices De Correlacion Financiera

Author

Listed:
  • Linda Margarita Medina Herrera
  • Ernesto Armando Pacheco Velazquez

Abstract

This paper uses the theory of random matrices and minimal spanning trees to analyze the correlation matrix C of returns of the top 35 stocks traded on the Mexican Stock Market. The results show the spectrum of the matrix C has a random band structure. The eigenvector components outside this band show significant similarities to the topological measures of the minimum spanning tree. The telecommunications company AMX is the central vertex of the tree and the main component of the largest eigenvector. The tree measures support the conclusion that only two clusters are formed by economic sectors: construction & telecommunications, which have a great influence on other stocks.

Suggested Citation

  • Linda Margarita Medina Herrera & Ernesto Armando Pacheco Velazquez, 2013. "Spectral Analysis And Networks In Financial Correlation Matrices, Analisis Espectral Y Redes En Matrices De Correlacion Financiera," Revista Internacional Administracion & Finanzas, The Institute for Business and Finance Research, vol. 6(6), pages 15-28.
    • Handle: RePEc:ibf:riafin:v:6:y:2013:i:6:p:15-28
    as

    Download full text from publisher

    File URL: http://www.theibfr2.com/RePEc/ibf/riafin/riaf-v6n6-2013/RIAF-V6N6-2013-2.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Sergei Maslov, 2001. "Measures of globalization based on cross-correlations of world financial indices," Papers cond-mat/0103397, arXiv.org, revised Apr 2001.
    3. Varsha Kulkarni & Nivedita Deo, 2007. "Correlation and volatility in an Indian stock market: A random matrix approach," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 60(1), pages 101-109, November.
    4. Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1999. "Random matrix theory and financial correlations," Science & Finance (CFM) working paper archive 500053, Science & Finance, Capital Fund Management.
    5. Plerou, V & Gopikrishnan, P & Rosenow, B & Amaral, L.A.N & Stanley, H.E, 2000. "A random matrix theory approach to financial cross-correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 287(3), pages 374-382.
    6. Laurent Laloux & Pierre Cizeau & Jean-Philippe Bouchaud & Marc Potters, 1999. "Random matrix theory," Science & Finance (CFM) working paper archive 500052, Science & Finance, Capital Fund Management.
    7. Barthélemy, Marc & Barrat, Alain & Pastor-Satorras, Romualdo & Vespignani, Alessandro, 2005. "Characterization and modeling of weighted networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 346(1), pages 34-43.
    8. J.-P. Bouchaud & L. Laloux & M. A. Miceli & M. Potters, 2007. "Large dimension forecasting models and random singular value spectra," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 55(2), pages 201-207, January.
    9. Maslov, Sergei, 2001. "Measures of globalization based on cross-correlations of world financial indices," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 301(1), pages 397-406.
    10. Giovanni Bonanno & Nicolas Vandewalle & Rosario N. Mantegna, 2000. "Taxonomy of Stock Market Indices," Papers cond-mat/0001268, arXiv.org, revised Aug 2000.
    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. Leonidas Sandoval Junior & Italo De Paula Franca, 2011. "Correlation of financial markets in times of crisis," Papers 1102.1339, arXiv.org, revised Mar 2011.
    2. 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.
    3. 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.
    4. Radhakrishnan, Srinivasan & Duvvuru, Arjun & Sultornsanee, Sivarit & Kamarthi, Sagar, 2016. "Phase synchronization based minimum spanning trees for analysis of financial time series with nonlinear correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 444(C), pages 259-270.
    5. Gautier Marti & Frank Nielsen & Miko{l}aj Bi'nkowski & Philippe Donnat, 2017. "A review of two decades of correlations, hierarchies, networks and clustering in financial markets," Papers 1703.00485, arXiv.org, revised Nov 2020.
    6. Tao You & Paweł Fiedor & Artur Hołda, 2015. "Network Analysis of the Shanghai Stock Exchange Based on Partial Mutual Information," JRFM, MDPI, vol. 8(2), pages 1-19, June.
    7. 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 (2007-2020), Kiel Institute for the World Economy (IfW Kiel), vol. 6, pages 1-81.
    8. Zhang, Yiting & Lee, Gladys Hui Ting & Wong, Jian Cheng & Kok, Jun Liang & Prusty, Manamohan & Cheong, Siew Ann, 2011. "Will the US economy recover in 2010? A minimal spanning tree study," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 390(11), pages 2020-2050.
    9. Stosic, Darko & Stosic, Dusan & Ludermir, Teresa B. & Stosic, Tatijana, 2018. "Collective behavior of cryptocurrency price changes," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 507(C), pages 499-509.
    10. Duc Thi Luu, 2022. "Portfolio Correlations in the Bank-Firm Credit Market of Japan," Computational Economics, Springer;Society for Computational Economics, vol. 60(2), pages 529-569, August.
    11. James, Nick & Menzies, Max & Gottwald, Georg A., 2022. "On financial market correlation structures and diversification benefits across and within equity sectors," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 604(C).
    12. Agne Reklaite, 2015. "Globalisation Effect Measure Via Hierarchical Dynamic Factor Modelling," Equilibrium. Quarterly Journal of Economics and Economic Policy, Institute of Economic Research, vol. 10(3), pages 139-149, September.
    13. Sensoy, Ahmet & Tabak, Benjamin M., 2014. "Dynamic spanning trees in stock market networks: The case of Asia-Pacific," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 414(C), pages 387-402.
    14. 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.
    15. Lahmiri, Salim & Uddin, Gazi Salah & Bekiros, Stelios, 2017. "Clustering of short and long-term co-movements in international financial and commodity markets in wavelet domain," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 486(C), pages 947-955.
    16. Núñez-Mora, José Antonio & Mata-Mata, Leovardo, 2014. "Una aplicación de la teoría de matrices aleatorias para analizar la variación del rendimiento de diferentes commodities a lo largo del periodo 2000-2012," eseconomía, Escuela Superior de Economía, Instituto Politécnico Nacional, vol. 0(41), pages 7-20, segundo s.
    17. Juan Pineiro-Chousa & Marcos Vizcaíno-González & Jérôme Caby, 2016. "Analysing voting behaviour in the United States banking sector through eigenvalue decomposition," Applied Economics Letters, Taylor & Francis Journals, vol. 23(12), pages 840-843, August.
    18. Tabak, Benjamin M. & Serra, Thiago R. & Cajueiro, Daniel O., 2009. "The expectation hypothesis of interest rates and network theory: The case of Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(7), pages 1137-1149.
    19. Kim, Kyungwon & Jung, Sean S., 2014. "Empirical analysis of structural change in Credit Default Swap volatility," Chaos, Solitons & Fractals, Elsevier, vol. 60(C), pages 56-67.
    20. Miśkiewicz, Janusz & Ausloos, Marcel, 2010. "Has the world economy reached its globalization limit?," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(4), pages 797-806.

    More about this item

    Keywords

    Random Matrix Theory; Stock Market Network; Econophysics; Minimum Spanning Tree;
    All these keywords.

    JEL classification:

    • C16 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Econometric and Statistical Methods; Specific Distributions
    • C65 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Miscellaneous Mathematical Tools
    • G11 - Financial Economics - - General Financial Markets - - - Portfolio Choice; Investment Decisions
    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics
    • C22 - Mathematical and Quantitative Methods - - Single Equation Models; Single Variables - - - Time-Series Models; Dynamic Quantile Regressions; Dynamic Treatment Effect Models; Diffusion Processes
    • C38 - Mathematical and Quantitative Methods - - Multiple or Simultaneous Equation Models; Multiple Variables - - - Classification Methdos; Cluster Analysis; Principal Components; Factor Analysis
    • C45 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: Special Topics - - - Neural Networks and Related Topics
    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • C8 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs
    • D85 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Network Formation

    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:ibf:riafin:v:6:y:2013:i:6:p:15-28. 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: Mercedes Jalbert (email available below). General contact details of provider: .

    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.