Correlation, Hierarchies, and Networks in Financial Markets
Carnegie Mellon University - Department of Social and Decision Sciences; University of Palermo
University of Palermo
Rosario N. Mantegna
Central European University; University of Palermo
September 28, 2009
Journal of Economic Behavior and Organization, Forthcoming
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.
Number of Pages in PDF File: 38
Keywords: Multivariate Analysis, Hierarchical Clustering, Correlation Based Networks, Bootstrap Validation, Factor Models, Kullback-Leibler Distance
JEL Classification: C32, G10Accepted Paper Series
Date posted: May 29, 2010
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