# 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.

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