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

TL;DR

This paper introduces a novel network-based method to compare series of rankings with ties, applying it to analyze stock market data and extending Kendall's coefficient for partial rankings.

Contribution

It extends the concept of Competitivity Graph and Kendall's coefficient to handle ties and series of rankings using a multiplex network framework.

Findings

Effective comparison of stock rankings over time

New method for handling ties based on thresholds

Insights into IBEX-35 stock dynamics from 2003-2013

Abstract

In this paper we extend the concept of Competitivity Graph to compare series of rankings with ties ({\em 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 {\em 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.