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

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 coe cient for two partial rankings to the concept of evolutive Kendall's coe cient 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 de ne 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 de ned by 25 companies that have contributed to the IBEX-35 return and volatility values over the period 2003 to 2013.