# Optimal decision for the market graph identification problem in a sign similarity network

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## Abstract

Research into the market graph is attracting increasing attention in stock market analysis. One of the important problems connected with the market graph is its identification from observations. The standard way of identifying the market graph is to use a simple procedure based on statistical estimations of Pearson correlations between pairs of stocks. Recently a new class of statistical procedures for market graph identification was introduced and the optimality of these procedures in the Pearson correlation Gaussian network was proved. However, the procedures obtained have a high reliability only for Gaussian multivariate distributions of stock attributes. One of the ways to correct this problem is to consider different networks generated by different measures of pairwise similarity of stocks. A new and promising model in this context is the sign similarity network. In this paper the market graph identification problem in the sign similarity network is reviewed. A new class of statistical procedures for the market graph identification is introduced and the optimality of these procedures is proved. Numerical experiments reveal an essential difference in the quality between optimal procedures in sign similarity and Pearson correlation networks. In particular, it is observed that the quality of the optimal identification procedure in the sign similarity network is not sensitive to the assumptions on the distribution of stock attributes.

## Keywords

Pearson correlation network Sign similarity network Market graph Multiple decision statistical procedures Loss function Risk function Optimal multiple decision procedures## Notes

### Acknowledgements

The work has been conducted at the Laboratory of Algorithms and Technologies for Network Analysis of the National Research University Higher School of Economics. V. A. Kalyagin and A. P. Koldanov are partially supported by RFFI Grant 14-01-00807, and P. A. Koldanov is partially supported by RFHR Grant 15-32-01052.

## References

- Bautin, G. A., Kalyagin, V. A., & Koldanov, A. P. (2013). Comparative analysis of two similarity measures for the market graph construction. In
*Proceedings in mathematics and statistics*(Vol. 59, pp. 29–41). Springer.Google Scholar - Bautin, G. A., Kalyagin, V. A., Koldanov, A. P., Koldanov, P. A., & Pardalos, P. M. (2013). Simple measure of similarity for the market graph construction.
*Computational Management Science*,*10*, 105–124.CrossRefGoogle Scholar - Boginsky, V., Butenko, S., & Pardalos, P. M. (2003). On structural properties of the market graph. In A. Nagurney (Ed.),
*Innovations in financial and economic networks*(pp. 29–45). Northampton: Edward Elgar Publishing Inc.Google Scholar - Boginsky, V., Butenko, S., & Pardalos, P. M. (2004). Network model of massive data sets.
*Computer Science and Information Systems*,*1*, 75–89.CrossRefGoogle Scholar - Boginsky, V., Butenko, S., & Pardalos, P. M. (2005). Statistical analysis of financial networks.
*Journal of Computational Statistics and Data Analysis*,*48*(2), 431–443.CrossRefGoogle Scholar - Boginsky, V., Butenko, S., & Pardalos, P. M. (2006). Mining market data: a network approach.
*J. Computers and Operations Research.*,*33*(11), 3171–3184.CrossRefGoogle Scholar - Boginski, V., Butenko, S., Shirokikh, O., Trukhanov, S., & Lafuente, J. G. (2014). A network-based data mining approach to portfolio selection via weighted clique relaxations.
*Annals of Operations Research*,*216*, 23–34.CrossRefGoogle Scholar - Cesarone, F., Scozzari, A., & Tardella, F. (2015). A new method for mean-variance portfolio optimization with cardinality constraints.
*Annals of Operations Research*,*215*, 213–234.Google Scholar - Emmert-Streib, F., & Dehmer, M. (2010). Identifying critical financial networks of the DJIA: Towards a network based index.
*Complexity*,*16*(1), 24–33.Google Scholar - Garas, F., & Argyrakis, P. (2007). Correlation study of the Athens stock exchange.
*Physica A*,*380*, 399–410.CrossRefGoogle Scholar - Gunawardena, A. D. A., Meyer, R. R., Dougan, W. L., Monaghan, P. E., & ChotonBasu, P. E. M. (2012). Optimal selection of an independent set of cliques in a market graph. In:
*International proceedings of economics development and research*(Vol. 29, p. 281285).Google Scholar - Gupta, F. K., Varga, T., & Bodnar, T. (2013).
*Elliptically contoured models in statistics and portfolio theory*. New York: Springer.CrossRefGoogle Scholar - Hero, A., & Rajaratnam, B. (2012). Hub discovery in partial correlation graphs.
*IEEE Transactions on Information Theory*,*58*(9), 6064–6078.CrossRefGoogle Scholar - Huang, W. Q., Zhuang, X. T., & Yao, S. A. (2009). A network analysis of the Chinese stock market.
*Physica A*,*388*, 2956–2964.CrossRefGoogle Scholar - Huffner, F., Komusiewicz, C., Moser, H., & Niedermeier, R. (2008). Enumerating isolated cliques in synthetic and financial networks. In
*Combinatorial optimization and applications, lecture notes in computer science*(Vol. 5165, pp. 405–416).Google Scholar - Kalyagin, V. A., Koldanov, A. P., & Koldanov, P. A. (2017). Robust identification in random variables networks.
*Journal of Statistical Planning and Inference*,*181*(2017), 30–40.CrossRefGoogle Scholar - Kenett, D. Y., Tumminello, M., Madi, A., Gur-Gershgoren, G., Mantegna, R. N., & Ben-Jacob, E. (2010). Dominating clasp of the financial sector revealed by partial correlation analysis of the stock market.
*PLoS ONE*,*5*(12), e15032. doi: 10.1371/journal.pone.0015032.CrossRefGoogle Scholar - Koldanov, A. P., Koldanov, P. A., Kalyagin, V. A., & Pardalos, P. M. (2013). Statistical procedures for the market graph construction.
*Computational Statistics and Data Analysis*,*68*, 17–29.CrossRefGoogle Scholar - Kramer, H. (1962).
*Mathematical methods of statistics*(9th ed.). Princeton: Princeton University Press.Google Scholar - Lehmann, E. L. (1957). A theory of some multiple decision procedures 1.
*Annals of Mathematical Statistics*,*28*, 1–25.CrossRefGoogle Scholar - Lehmann, E. L., & Romano, J. P. (2005).
*Testing statistical hypotheses*. New York: Springer.Google Scholar - Mantegna, R. N. (1999). Hierarchical structure in financial markets.
*European Physical Journal, Series B*,*11*, 93–97.Google Scholar - Namaki, A., Shirazi, A. H., Raei, R., & Jafari, G. R. (2011). Network analysis of a financial market based on genuine correlation and threshold method.
*Physica A*,*390*, 3835–3841.CrossRefGoogle Scholar - Onella, J.-P., Kaski, K., & Kertesz, J. (2004). Clustering and information in correlation based financial networks.
*The European Physical Journal B-Condensed Matter and Complex Systems*,*38*(2), 353–362.CrossRefGoogle Scholar - Shirokikh, J., Pastukhov, G., Boginski, V., & Butenko, S. (2013). Computational study of the US stock market evolution: A rank correlation-based network model.
*Computational Management Science*,*10*(2–3), 81–103.CrossRefGoogle Scholar - Tse, C. K., Liu, J., & Lau, F. C. M. (2010). A network perspective of the stock market.
*Journal of Empirical Finance*,*17*, 659–667.CrossRefGoogle Scholar - Tumminello, M., Coronello, C., Lillo, F., Micciche, S., & Mantegna, R. (2007). Spanning trees and bootstrap reliability estimation in correlation-based network.
*International Journal of Bifurcation and Chaos*,*17*, 2319–2329.CrossRefGoogle Scholar - Vizgunov, A. N., Goldengorin, B., Kalyagin, V. A., Koldanov, A. P., Koldanov, P. A., & Pardalos, P. M. (2014). Network approach for the Russian stock market.
*Computational Management Science*,*11*, 45–55.CrossRefGoogle Scholar - Wald, A. (1950).
*Statistical decision function*. New York: Wiley.Google Scholar - Wang, G. J., Chi, X., Han, F., & Sun, B. (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*,*391*(16), 4136–4146.CrossRefGoogle Scholar - Wang, Z., Glynn, P. W., & Ye, Y. (2016). Likelihood robust optimization for data-driven problems.
*Computational Management Science*,*13*, 241–261.CrossRefGoogle Scholar