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

Investigation of the market graph attracts a growing attention in market network analysis. One of the important problem connected with market graph is to identify it from observations. Traditional way for the market graph identification 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 the market graph identification was introduced and optimality of these procedures in Pearson correlation Gaussian network was proved. However the obtained procedures have a high reliability only for Gaussian multivariate distributions of stocks attributes. One of the way to correct this drawback is to consider a 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 the present paper the market graph identification problem in sign similarity network is considered. A new class of statistical procedures for the market graph identification is introduced and optimality of these procedures is proved. Numerical experiments detect essential difference in quality of optimal procedures in sign similarity and Pearson correlation networks. In particular it is observed that the quality of optimal identification procedure in sign similarity network is not sensitive to the assumptions on distribution of stocks attributes.