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Statistical Procedures for Stock Markets Network Structures Identification

Author

Listed:
  • Kalyagin, V.

    (National Research University Higher School of Economics, Nijni Novgorod, Russia)

  • Koldanov, A.

    (National Research University Higher School of Economics, Nijni Novgorod, Russia)

  • Koldanov, P.

    (National Research University Higher School of Economics, Nijni Novgorod, Russia)

  • Pardalos, P.

    (University of Florida, USA)

Abstract

Network (graphical) model of stock market is a complete weighted graph. Nodes of the graph corresponds to the stocks and weights of edges are given by some measure of dependence between characteristics of the stocks. The most common characteristic of stocks is their return. In the analysis of network (graphical) models of returns of primary interest are network structures (subgraphs of a complete graph), containing key information about the considered network. Popular network structures are the minimum spanning tree, planar maximally filtered graph, market graph, a cliques and an independent set of the market graph. The problem of identification of network structure is to define the structure from observations. An important characteristic of identification statistical procedure is its uncertainty related with finite sample size. Significant role in this play the joint distribution of returns and the choice of measures of dependence between them. The most common measure of dependence is Pearson's correlation. A wide class of joint distributions of stock returns is represented by elliptical models. However, the procedures based on Pearson correlations are non robust when the joint distribution of returns is deviated from the normal in the class of elliptical distributions. The aim of this work is to present a general approach to construction of robust (distribution free) statistical procedures of identification of network structures. It is proposed to use the probability of sign coincidence of stock returns as a measure of dependence. It is shown that the single-step and stepwise standard procedure of identification of network structures based on the probability of sign coincidence are robust in the class of elliptical distributions. It allows to recommend these procedures for practical applications.

Suggested Citation

  • Kalyagin, V. & Koldanov, A. & Koldanov, P. & Pardalos, P., 2017. "Statistical Procedures for Stock Markets Network Structures Identification," Journal of the New Economic Association, New Economic Association, vol. 35(3), pages 33-52.
    • Handle: RePEc:nea:journl:y:2017:i:35:p:33-52
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    References listed on IDEAS

    as
    1. G. Bonanno & F. Lillo & R. N. Mantegna, 2001. "High-frequency cross-correlation in a set of stocks," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 96-104.
    2. R. Mantegna, 1999. "Hierarchical structure in financial markets," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 11(1), pages 193-197, September.
    3. Grigory Bautin & Valery Kalyagin & Alexander Koldanov & Petr Koldanov & Panos Pardalos, 2013. "Simple measure of similarity for the market graph construction," Computational Management Science, Springer, vol. 10(2), pages 105-124, June.
    4. Jung, Woo-Sung & Chae, Seungbyung & Yang, Jae-Suk & Moon, Hie-Tae, 2006. "Characteristics of the Korean stock market correlations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 361(1), pages 263-271.
    5. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. II," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 23(3), pages 98-132.
    6. C. Coronnello & M. Tumminello & F. Lillo & S. Miccich`e & R. N. Mantegna, 2005. "Sector identification in a set of stock return time series traded at the London Stock Exchange," Papers cond-mat/0508122, arXiv.org.
    7. Tumminello, Michele & Lillo, Fabrizio & Mantegna, Rosario N., 2010. "Correlation, hierarchies, and networks in financial markets," Journal of Economic Behavior & Organization, Elsevier, vol. 75(1), pages 40-58, July.
    8. Fantazzini, Dean, 2011. "Analysis of multidimensional probability distributions with copula functions. III," Applied Econometrics, Russian Presidential Academy of National Economy and Public Administration (RANEPA), vol. 24(4), pages 100-130.
    9. Boginski, Vladimir & Butenko, Sergiy & Pardalos, Panos M., 2005. "Statistical analysis of financial networks," Computational Statistics & Data Analysis, Elsevier, vol. 48(2), pages 431-443, February.
    10. Tabak, Benjamin M. & Serra, Thiago R. & Cajueiro, Daniel O., 2010. "Topological properties of stock market networks: The case of Brazil," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 389(16), pages 3240-3249.
    11. Garas, Antonios & Argyrakis, Panos, 2007. "Correlation study of the Athens Stock Exchange," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 380(C), pages 399-410.
    12. Huang, Wei-Qiang & Zhuang, Xin-Tian & Yao, Shuang, 2009. "A network analysis of the Chinese stock market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 388(14), pages 2956-2964.
    13. Harry Markowitz, 1952. "Portfolio Selection," Journal of Finance, American Finance Association, vol. 7(1), pages 77-91, March.
    14. Grigory A. Bautin & Alexander P. Koldanov & Panos M. Pardalos, 2014. "Robustness of Sign Correlation in Market Network Analysis," Springer Optimization and Its Applications, in: Valery A. Kalyagin & Panos M. Pardalos & Themistocles M. Rassias (ed.), Network Models in Economics and Finance, edition 127, pages 25-33, Springer.
    15. Vizgunov, A. & Goldengorin, B. & Zamaraev, V. & Kalyagin, V. & Koldanov, A. & Koldanov, P. & Pardalos, P., 2012. "Applying Market Graphs for Russian Stock Market Analysis," Journal of the New Economic Association, New Economic Association, vol. 15(3), pages 66-81.
    16. Wang, Gang-Jin & Xie, Chi & Han, Feng & Sun, Bo, 2012. "Similarity measure and topology evolution of foreign exchange markets using dynamic time warping method: Evidence from minimal spanning tree," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(16), pages 4136-4146.
    17. Ong Chong Tee, 2005. "The impact of globalisation on the formulation and implementation of monetary policy in Singapore," BIS Papers chapters, in: Bank for International Settlements (ed.), Globalisation and monetary policy in emerging markets, volume 23, pages 263-68, Bank for International Settlements.
    18. Bank for International Settlements, 2005. "Globalisation and monetary policy in emerging markets," BIS Papers, Bank for International Settlements, number 23, October –.
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    Cited by:

    1. Koldanov, A. & Koldanov, P. & Semenov, D., 2021. "Confidence set for connected stocks of stock market," Journal of the New Economic Association, New Economic Association, vol. 50(2), pages 12-34.

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    More about this item

    Keywords

    financial market; network (graphical) model; network structure; Pearson correlation; probability of sign coincidence;
    All these keywords.

    JEL classification:

    • C02 - Mathematical and Quantitative Methods - - General - - - Mathematical Economics

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