An uncertainty estimation of the conclusions about the Russian market structure

Student: Sizov Aleksandr

Faculty: Faculty of Informatics, Mathematics, and Computer Science (HSE Nizhny Novgorod)

Educational Programme: Master

Year of Graduation: 2014

Traditional methods of network analysis of stock markets mostly limited to solving complex computational problems associated with high dimensionality of analyzed structures. However, the random nature of the analyzed data inevitably leads to errors when making decisions, and consequently, to the statistical uncertainty of the obtained results. Therefore, it is important for us to know how much will be reliable the conclusions are obtained by analysis of different network structures: MST, MG, MC, MIS, PMFG, etc. On this basis we will be able to understand when and what to take network structure to obtain the most accurate results.To find the answer to this question was proposed approach based on the use of the concept of conditional risk of the statistical theory of making decisions for assessment of the statistical uncertainty of results obtained in the analysis of different network structures in [V. A. Kalyagin, Koldanov A. P., Koldanov P. A., P. M. Pardalos, Zamaraev V. A. Measures of uncertainty in market network analysis [Electronic resource] // arXiv. - URL: <a href="http://arxiv.org/pdf/1311.2273v1.pdf">http://arxiv.org/pdf/1311.2273v1.pdf</a>. - P. 1-23, 2013]. The methodology was applied to the analysis of the statistical uncertainty of the American stock market. The experimental results showed that the statistical uncertainty of a minimum spanning tree is much worse in comparison with the statistical uncertainty of the market graph. However, the results were obtained for the American stock market, perhaps, it does not mean that the same results we get for another stock market. The purpose of the study was to assess the statistical uncertainty of the Russian stock market and comparing the obtained results with those obtained for the American stock market in the previously mentioned article.Tasks that were set in the given work: <ol><li>Make a brief review of existing approaches to network analysis of financial markets. </li><li>Describe briefly a new method proposed in the article [V. A. Kalyagin, Koldanov A. P., Koldanov P. A., P. M. Pardalos, Zamaraev V. A. Measures of uncertainty in market network analysis [Electronic resource] // arXiv. - URL: <a href="http://arxiv.org/pdf/1311.2273v1.pdf">http://arxiv.org/pdf/1311.2273v1.pdf</a>. - P. 1-23, 2013], which is used to assess the statistical uncertainty in the market network analysis.</li><li>Apply this method for estimating the statistical uncertainty of the Russian stock market for a minimum spanning tree and market graph.</li><li>Compare the obtained results with the results of the American stock market in the article [V. A. Kalyagin, Koldanov A. P., Koldanov P. A., P. M. Pardalos, Zamaraev V. A. Measures of uncertainty in market network analysis [Electronic resource] // arXiv. - URL: <a href="http://arxiv.org/pdf/1311.2273v1.pdf">http://arxiv.org/pdf/1311.2273v1.pdf</a>. - P. 1-23, 2013]. </li></ol>Theoretical and methodological base of the research consists of works of Russian and foreign scientists on the application of various methods and techniques to network analysis of financial markets: V. A. Kalyagin, G. A. Bautin, P. M. Pardalos, A. P. Koldanov, P. A. Kolganov, R. N. Mantegna, M. A. Djauhari, M. Galazka, S. Chen, W.-J. Wang, B. M. Tabak and others.In the process of writing of this work were used the following methods of research: <ul><li>studying and analyzing of scientific articles by Russian and foreign authors on the application of different approaches and techniques to network analysis of stock markets;</li><li>probability theory and mathematical statistics for the simulating of random variables from a multivariate normal distribution with parameters corresponding to the choosen distribution and evaluating of obtained results.</li></ul>Computational experiments showed interesting results. When considering the Russian stock market the hypothesis concerning the fact that the statistical uncertainty of the minimum spanning tree should be an order of magnitude worse statistical uncertainty market graph, fully confirmed. However, if we take a few shares at random sense from the entire market, then the uncertainty will depend on the number and composition of selected stocks.

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