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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show all references

References:
[1]

The Economic Journal, 105 (1995), 864-880. doi: 10.2307/2235155.  Google Scholar

[2]

Journal of the ACM, 55 (2008), Art. 23, 27 pp. doi: 10.1145/1411509.1411513.  Google Scholar

[3]

Information Processing and Management, 41 (2005), 1511-1519. doi: 10.1016/j.ipm.2005.03.008.  Google Scholar

[4]

in Parameterized and Exact Computation, Lecture Notes in Computer Sciences, 6478, Springer, Berlin, 2010, 26-37. doi: 10.1007/978-3-642-17493-3_5.  Google Scholar

[5]

Graph Drawing, Lecture Notes in Computer Sciences, 3843, Springer, Berlin, 2006, 1-12. doi: 10.1007/11618058_1.  Google Scholar

[6]

Physics Reports, 544 (2014), 1-122. doi: 10.1016/j.physrep.2014.07.001.  Google Scholar

[7]

$8^{th}$ edition, Mc Graw-Hill, 2006. Google Scholar

[8]

South-Western, 2002. Google Scholar

[9]

in Proc. of the 32nd Int. ACM Conf. Research and Development in Information Retrieval, ACM, New York, 2009, 436-443. doi: 10.1145/1571941.1572017.  Google Scholar

[10]

Journal of Artificial Intelligence Research, 10 (1999), 243-270. doi: 10.1613/jair.587.  Google Scholar

[11]

in Proceedings of The Twenty-First National Conference on Artificial Intelligence and the Eighteenth Innovative Applications of Artificial Intelligence Conference, 2006, 620-626. Google Scholar

[12]

RAIRO, Recherche Operationelle/Operations Research, 20 (1986), 115-122.  Google Scholar

[13]

European Journal of Operational Research, 172 (2006), 369-385. doi: 10.1016/j.ejor.2005.03.048.  Google Scholar

[14]

Chaos: An Interdisciplinary Journal of Nonlinear Science, 23 (2013), 043114. doi: 10.1063/1.4826446.  Google Scholar

[15]

in Proc. 10th International Conference on World Wide Web, WWW'01, ACM, New York, 2001, 613-622. doi: 10.1145/371920.372165.  Google Scholar

[16]

J. Multi-Crit. Decis. Anal., 11 (2002), 17-28. doi: 10.1002/mcda.313.  Google Scholar

[17]

SIAM J. Discrete Math., 20 (2006), 628-648. doi: 10.1137/05063088X.  Google Scholar

[18]

Journal of Financial Economics, 33 (1993), 3-56. doi: 10.1016/0304-405X(93)90023-5.  Google Scholar

[19]

Discrete Mathematics, 43 (1983), 37-46. doi: 10.1016/0012-365X(83)90019-5.  Google Scholar

[20]

Sci. Rep., 2 (2012), 1-6. doi: 10.1038/srep00620.  Google Scholar

[21]

Physical Review Letters, 110 (2013), 028701. doi: 10.1103/PhysRevLett.110.028701.  Google Scholar

[22]

ACM Computing Surveys, 40 (2008), p11. doi: 10.1145/1391729.1391730.  Google Scholar

[23]

, Invertia, The Economical Website of Telefónica (Spain)., Available from: , ().   Google Scholar

[24]

in Algorithms and computation. Part I, Lecture Notes in Computer Science, 6506, Springer, Berlin, 2010, 3-14. doi: 10.1007/978-3-642-17517-6_3.  Google Scholar

[25]

$2^{nd}$ edition, The MIT Press, Cambridge, 1978.  Google Scholar

[26]

Biometrika, 30 (1938), 81-93. doi: 10.1093/biomet/30.1-2.81.  Google Scholar

[27]

Ann. Math. Statist., 10 (1939), 275-287. doi: 10.1214/aoms/1177732186.  Google Scholar

[28]

SIAM J. Comput., 36 (2006), 326-353. doi: 10.1137/S0097539703437855.  Google Scholar

[29]

in Proc. 19th International Conference on World Wide Web, WWW'10, ACM, New York, 2010, 571-580. doi: 10.1145/1772690.1772749.  Google Scholar

[30]

$1^{st}$ edition, Princeton University Press, New Jersey, 2012. Google Scholar

[31]

, Madrid Stock Market, Official Annual Reports about Madrid and Spanish Stock Markets (in Spanish)., Available from: , ().   Google Scholar

[32]

Wiley, Somerset, NJ, 1991. Google Scholar

[33]

Canadian Journal of Mathematics, 23 (1971), 160-175. doi: 10.4153/CJM-1971-016-5.  Google Scholar

[34]

The Journal of Futures Markets, 8 (1988), 271-290. doi: 10.1002/fut.3990080303.  Google Scholar

[35]

International Studies Quarterly, 43 (1999), 115-144. doi: 10.1111/0020-8833.00113.  Google Scholar

[36]

ACM Transactions on Database Systems, 36 (2011), p19. doi: 10.1145/2000824.2000829.  Google Scholar

[37]

Proceedings of the National Academy of Sciences, 107 (2010), 13636-13641. doi: 10.1073/pnas.1004008107.  Google Scholar

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