IDEAS home Printed from https://ideas.repec.org/
MyIDEAS: Login to save this article or follow this journal

Correlation, hierarchies, and networks in financial markets

  • Tumminello, Michele
  • Lillo, Fabrizio
  • Mantegna, Rosario N.

We discuss some methods to quantitatively investigate the properties of correlation matrices. Correlation matrices play an important role in portfolio optimization and in several other quantitative descriptions of asset price dynamics in financial markets. Here, we discuss how to define and obtain hierarchical trees, correlation based trees and networks from a correlation matrix. The hierarchical clustering and other procedures performed on the correlation matrix to detect statistically reliable aspects of it are seen as filtering procedures of the correlation matrix. We also discuss a method to associate a hierarchically nested factor model to a hierarchical tree obtained from a correlation matrix. The information retained in filtering procedures and its stability with respect to statistical fluctuations is quantified by using the Kullback-Leibler distance.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL: http://www.sciencedirect.com/science/article/B6V8F-4Y70C2G-3/2/096ef02707b1fb9e4fb7aea7e24d9104
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Journal of Economic Behavior & Organization.

Volume (Year): 75 (2010)
Issue (Month): 1 (July)
Pages: 40-58

as
in new window

Handle: RePEc:eee:jeborg:v:75:y:2010:i:1:p:40-58
Contact details of provider: Web page: http://www.elsevier.com/locate/jebo

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

as in new window
  1. Olivier Ledoit & Michael Wolf, 2001. "Improved estimation of the covariance matrix of stock returns with an application to portofolio selection," Economics Working Papers 586, Department of Economics and Business, Universitat Pompeu Fabra.
  2. S. Illeris & G. Akehurst, 2001. "Introduction," The Service Industries Journal, Taylor & Francis Journals, vol. 21(1), pages 1-4, January.
  3. M. Tumminello & F. Lillo & R. N. Mantegna, 2007. "Shrinkage and spectral filtering of correlation matrices: a comparison via the Kullback-Leibler distance," Papers 0710.0576, arXiv.org.
  4. Michele Tumminello & Fabrizio Lillo & Rosario Nunzio Mantegna, 2007. "Kullback-Leibler distance as a measure of the information filtered from multivariate data," Papers 0706.0168, arXiv.org.
  5. Rosario N. Mantegna, 1998. "Hierarchical Structure in Financial Markets," Papers cond-mat/9802256, arXiv.org.
  6. Tola, Vincenzo & Lillo, Fabrizio & Gallegati, Mauro & Mantegna, Rosario N., 2008. "Cluster analysis for portfolio optimization," Journal of Economic Dynamics and Control, Elsevier, vol. 32(1), pages 235-258, January.
  7. Marc Potters & Jean-Philippe Bouchaud & Laurent Laloux, 2005. "Financial Applications of Random Matrix Theory: Old Laces and New Pieces," Science & Finance (CFM) working paper archive 500058, Science & Finance, Capital Fund Management.
  8. Salvatore Miccich\`e & Giovanni Bonanno & Fabrizio Lillo & Rosario N. Mantegna, 2002. "Degree stability of a minimum spanning tree of price return and volatility," Papers cond-mat/0212338, arXiv.org.
  9. 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.
  10. M. Tumminello & T. Di Matteo & T. Aste & R. N. Mantegna, 2007. "Correlation based networks of equity returns sampled at different time horizons," The European Physical Journal B - Condensed Matter and Complex Systems, Springer, vol. 55(2), pages 209-217, 01.
  11. C. Coronnello & M. Tumminello & F. Lillo & S. Miccich\`e & R. N. Mantegna, 2005. "Sector identification in a set of stock return time series traded at the London Stock Exchange," Papers cond-mat/0508122, arXiv.org.
  12. Giulio Biroli & Jean-Philippe Bouchaud & Marc Potters, 2007. "The Student ensemble of correlation matrices: eigenvalue spectrum and Kullback-Leibler entropy," Papers 0710.0802, arXiv.org.
  13. Schäfer Juliane & Strimmer Korbinian, 2005. "A Shrinkage Approach to Large-Scale Covariance Matrix Estimation and Implications for Functional Genomics," Statistical Applications in Genetics and Molecular Biology, De Gruyter, vol. 4(1), pages 1-32, November.
  14. 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)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:jeborg:v:75:y:2010:i:1:p:40-58. 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: (Zhang, Lei)

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 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.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.