Statistical uncertainty of minimum spanning tree in market network
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.
Problem of construction of the market graph as a multiple decision statistical problem is considered. Detailed description of a optimal unbiased multiple decision statistical procedure is given. This procedure is constructed using the Lehmann’s theory of multiple decision statistical procedures and the conditional tests of the Neyman structures. The equations for thresholds calculation for the tests of the Neyman structure are presented and analyzed.
The main goal of the present paper is the development of general approach to network analysis of statistical data sets. First a general method of market network construction is proposed on the base of idea of measures of association. It is noted that many existing network models can be obtained as a particular case of this method. Next it is shown that statistical multiple decision theory is an appropriate theoretical basis for market network analysis of statistical data sets. Finally conditional risk for multiple decision statistical procedures is introduced as a natural measure of quality in market network analysis. Some illustrative examples are given.
Using network models to investigate the interconnectivity in modern economic systems allows researchers to better understand and explain some economic phenomena. This volume presents contributions by known experts and active researchers in economic and financial network modeling. Readers are provided with an understanding of the latest advances in network analysis as applied to economics, finance, corporate governance, and investments. Moreover, recent advances in market network analysis that focus on influential techniques for market graph analysis are also examined. Young researchers will find this volume particularly useful in facilitating their introduction to this new and fascinating field. Professionals in economics, financial management, various technologies, and network analysis, will find the network models presented in this book beneficial in analyzing the interconnectivity in modern economic systems.