6533b823fe1ef96bd127e091

RESEARCH PRODUCT

Hierarchically nested factor model from multivariate data

Fabrizio LilloFabrizio LilloMichele TumminelloRosario N. Mantegna

subject

Data recordsStructure (mathematical logic)Multivariate statisticsCovariance matrixFinance commerce hierarchical structureGeneral Physics and AstronomySimilarity matrixFOS: Physical sciencesDisordered Systems and Neural Networks (cond-mat.dis-nn)Condensed Matter - Disordered Systems and Neural Networkscomputer.software_genreHierarchical clusteringCondensed Matter - Other Condensed MatterSet (abstract data type)Factor (programming language)Data miningcomputerMathematicscomputer.programming_languageOther Condensed Matter (cond-mat.other)

description

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.

yearjournalcountryeditionlanguage
2005-11-30
https://dx.doi.org/10.48550/arxiv.cond-mat/0511726