Hierarchically nested factor model from multivariate dataM. Tumminello1, F. Lillo1, 2 and R. N. Mantegna1
1 Dipartimento di Fisica e Tecnologie Relative, Università di Palermo - Viale delle Scienze, I-90128 Palermo, Italy
2 Santa Fe Institute - 1399 Hyde Park Road, Santa Fe, NM 87501, USA
received 21 December 2006; accepted in final form 26 March 2007; published May 2007
published online 27 April 2007
We 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.
89.75.-k - Complex systems.
89.65.Gh - Economics; econophysics, financial markets, business and management.
© Europhysics Letters Association 2007