Correlation, hierarchies, and networks in financial markets
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Economic Behavior & Organization.
Volume (Year): 75 (2010)
Issue (Month): 1 (July)
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Web page: http://www.elsevier.com/locate/jebo
Multivariate analysis Hierarchical clustering Correlation based networks Bootstrap validation Factor models Kullback-Leibler distance;
Other versions of this item:
- M. Tumminello & F. Lillo & R. N. Mantegna, 2008. "Correlation, hierarchies, and networks in financial markets," Papers 0809.4615, arXiv.org.
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.:
- 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.
- 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.
- 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.
- G. Bonanno & F. Lillo & R. N. Mantegna, 2001.
"High-frequency cross-correlation in a set of stocks,"
Taylor and Francis Journals, vol. 1(1), pages 96-104.
- Giovanni Bonanno & Fabrizio Lillo & Rosario N. Mantegna, 2000. "High-frequency Cross-correlation in a Set of Stocks," Papers cond-mat/0009350, arXiv.org, revised Nov 2000.
- Vincenzo Tola & Fabrizio Lillo & Mauro Gallegati & Rosario N. Mantegna, 2005.
"Cluster analysis for portfolio optimization,"
- Ledoit, Olivier & Wolf, Michael, 2003.
"Improved estimation of the covariance matrix of stock returns with an application to portfolio selection,"
Journal of Empirical Finance,
Elsevier, vol. 10(5), pages 603-621, December.
- 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.
- 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.
- S. Illeris & G. Akehurst, 2001. "Introduction," The Service Industries Journal, Taylor and Francis Journals, vol. 21(1), pages 1-4, January.
- Salvatore Miccich\`e & Giovanni Bonanno & Fabrizio Lillo & Rosario N. Mantegna, 2002.
"Degree stability of a minimum spanning tree of price return and volatility,"
- 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.
- 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.
- 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.
- M. Tumminello & T. Di Matteo & T. Aste & R. N. Mantegna, 2006. "Correlation based networks of equity returns sampled at different time horizons," Papers physics/0605251, arXiv.org, revised Apr 2007.
- 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.
- M. Potters & J. P. Bouchaud & L. Laloux, 2005. "Financial Applications of Random Matrix Theory: Old Laces and New Pieces," Papers physics/0507111, arXiv.org.
- Giovanni Bonanno & Nicolas Vandewalle & Rosario N. Mantegna, 2000. "Taxonomy of Stock Market Indices," Papers cond-mat/0001268, arXiv.org, revised Aug 2000.
- 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.
- Sandoval, Leonidas, 2012. "Pruning a minimum spanning tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(8), pages 2678-2711.
- Vizgunov, A. & Goldengorin, B. & Zamaraev, V. & Kalyagin, V. & Koldanov, A. & Koldanov, P. & Pardalos, P., 2012. "Applying Market Graphs for Russian Stock Market Analysis," Journal of the New Economic Association, New Economic Association, vol. 15(3), pages 66-81.
- Leonidas Sandoval Junior, 2011. "A Map of the Brazilian Stock Market," Papers 1107.4146, arXiv.org, revised Mar 2013.
- Tiago Trancoso, 2013. "Global macroeconomic interdependence: a minimum spanning tree approach," Review of Applied Socio-Economic Research, Pro Global Science Association, vol. 5(1), pages 179-189, June.
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