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

Francisco Pedroche; Regino Criado; Esther García; Miguel Romance; Victoria E. Sánchez

doi:10.3934/nhm.2015.10.101

Article Contents

2015, Volume 10, Issue 1: 101-125. Doi: 10.3934/nhm.2015.10.101

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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
2.
Departamento de Matemática Aplicada, Ciencia e Ingeniería de los Materiales y Tecnología Electrónica, Universidad Rey Juan Carlos, 28933 Móstoles (Madrid)
3.
Departamento de Economía de la Empresa, Universidad Carlos III, 28903 Getafe (Madrid)

Received: July 2014

Revised: December 2014

Published: March 2015

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Abstract

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.

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Mathematics Subject Classification: Primary: 05C75, 94C15; Secondary: 05C82.

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