Correlation, Hierarchies, and Networks in Financial Markets

38 Pages Posted: 29 May 2010

See all articles by Michele Tumminello

Michele Tumminello

University of Palermo; Carnegie Mellon University - Department of Social and Decision Sciences

Fabrizio Lillo

Università di Bologna

Rosario N. Mantegna

University of Palermo

Date Written: September 28, 2009

Abstract

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. Specifically, 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.

Keywords: Multivariate Analysis, Hierarchical Clustering, Correlation Based Networks, Bootstrap Validation, Factor Models, Kullback-Leibler Distance

JEL Classification: C32, G10

Suggested Citation

Tumminello, Michele and Lillo, Fabrizio and Mantegna, Rosario Nunzio, Correlation, Hierarchies, and Networks in Financial Markets (September 28, 2009). Journal of Economic Behavior and Organization, Forthcoming. Available at SSRN: https://ssrn.com/abstract=1617257

Michele Tumminello

University of Palermo ( email )

Viale delle Scienza
Palermo, Palermo 90128
Italy

Carnegie Mellon University - Department of Social and Decision Sciences ( email )

Pittsburgh, PA 15213-3890
United States

Fabrizio Lillo

Università di Bologna ( email )

Via Zamboni, 33
Bologna, 40126
Italy

Rosario Nunzio Mantegna (Contact Author)

University of Palermo ( email )

Dipartimento di Fisica e Chimica
Viale delle Scienze, Edificio 18
Palermo, PA I-90128
Italy
+3909123899074 (Phone)
+3909123860815 (Fax)

HOME PAGE: http://www.unipa.it/persone/docenti/m/rosario.mantegna

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