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# Market graph construction based on partition correlation coefficient

Student: Ivan Grechikhin

Supervisor:

Educational Programme: Bachelor

<p>In this work, the problem of market graph construction is considered. In particular, partition correlation coefficient is described and analyzed. Market graph construction is a widely used technique in the modern analysis of stock market. Market graphs can help to analyze dependencies between stocks and to find some interesting characteristics of the network. The most popular measure of dependency between random variables or stocks in stock market is Pearson correlation coefficient. In order to analyze hypothesis about dependencies and values of coefficients such as Pearson correlation coefficient, there is a multiple-test. In short words, it can be described as test, which checks every distinct coefficient between two random variables without considering the influence of other random variables. In this work, we show that there is a test, which is better for checking the independency of random variables than multiple-test.</p><p>The work starts with detailed description about the procedure of constructing market graphs. In the second chapter, basic definitions and notations are given, which are used in this work. In chapter 3, we talk more about tests to check different hypothesis in market graphs. In particular, we talk about multiple-test and maximum likelihood test for the problem of independency of random variables and we compare both tests power functions. In chapter 4, there are more information about partition correlation coefficient, also, there are some explanations about meanings of partition correlation coefficient. In chapter 5, the connection between inverse correlation matrix and partition correlation coefficient is shown.</p><p>As a result, we have found, that maximum likelihood test is better than multiple-test for the hypothesis of independency of random variables for many alternatives. Also, partition correlation coefficient was analyzed as a measure of dependency between random variables.</p>

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