Статистические процедуры идентификации сетевых структур фондовых рынков

Abstract

Network (graphical) model of stock market is a complete weighted graph. Nodes of the graph corresponds to the stocks and weights of edges are given by some measure of dependence between characteristics of the stocks. The most common characteristic of stocks is their return. In the analysis of network (graphical) models of returns of primary interest are network structures (subgraphs of a complete graph), containing key information about the considered network. Popular network structures are the minimum spanning tree, planar maximally filtered graph, market graph, a cliques and an independent set of the market graph. The problem of identification of network structure is to define the structure from observations. An important characteristic of identification statistical procedure is its uncertainty related with finite sample size. Significant role in this play the joint distribution of returns and the choice of measures of dependence between them. The most common measure of dependence is Pearson's correlation. A wide class of joint distributions of stock returns is represented by elliptical models. However, the procedures based on Pearson correlations are non robust when the joint distribution of returns is deviated from the normal in the class of elliptical distributions. The aim of this work is to present a general approach to construction of robust (distribution free) statistical procedures of identification of network structures. It is proposed to use the probability of sign coincidence of stock returns as a measure of dependence. It is shown that the single-step and stepwise standard procedure of identification of network structures based on the probability of sign coincidence are robust in the class of elliptical distributions. It allows to recommend these procedures for practical applications.