American Institute of Mathematical Sciences

March  2015, 10(1): 101-125. doi: 10.3934/nhm.2015.10.101

Comparing series of rankings with ties by using complex networks: An analysis of the Spanish stock market (IBEX-35 index)

 1 Institut de Matemàtica Multidisciplinària, Universitat Politècnica de València, 46022 Valencia, Spain 2 Departamento de Matemática Aplicada, Ciencia e Ingeniería de los Materiales y Tecnología Electrónica, Universidad Rey Juan Carlos, 28933 Móstoles (Madrid), Spain 3 Departamento de Economía de la Empresa, Universidad Carlos III, 28903 Getafe (Madrid), Spain

Received  July 2014 Revised  December 2014 Published  February 2015

In this paper we extend the concept of Competitivity Graph to compare series of rankings with ties ( partial rankings). We extend the usual method used to compute Kendall's coefficient for two partial rankings to the concept of evolutive Kendall's coefficient for a series of partial rankings. The theoretical framework consists of a four-layer multiplex network. Regarding the treatment of ties, our approach allows to define a tie between two values when they are close enough, depending on a threshold. We show an application using data from the Spanish Stock Market; we analyse the series of rankings defined by $25$ companies that have contributed to the IBEX-35 return and volatility values over the period 2003 to 2013.
Citation: Francisco Pedroche, Regino Criado, Esther García, Miguel Romance, Victoria E. Sánchez. Comparing series of rankings with ties by using complex networks: An analysis of the Spanish stock market (IBEX-35 index). Networks & Heterogeneous Media, 2015, 10 (1) : 101-125. doi: 10.3934/nhm.2015.10.101
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References:
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