M. Tumminello et al 2007 EPL 78 30006 doi:10.1209/0295-5075/78/30006
M. Tumminello1, F. Lillo1,2 and R. N. Mantegna1
Show affiliationsWe show how to achieve a statistical description of the hierarchical structure of a multivariate data set. Specifically, we show that the similarity matrix resulting from a hierarchical clustering procedure is the correlation matrix of a factor model, the hierarchically nested factor model. In this model, factors are mutually independent and hierarchically organized. Finally, we use a bootstrap-based procedure to reduce the number of factors in the model with the aim of retaining only those factors significantly robust with respect to the statistical uncertainty due to the finite length of data records.
02.50.Sk Multivariate analysis
89.65.Gh Economics; econophysics, financial markets, business and management
Issue 3 (May 2007)
Received 21 December 2006, in final form 26 March 2007
Published 27 April 2007
M. Tumminello et al 2007 EPL 78 30006
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