توصیف بازارهای نوظهور سهام اروپا از طریق شبکه های پیچیده: از ویژگیهای محلی تا ویژگی های مشابه

We investigate the properties of the returns of the main emerging stock markets from Europe by means of complex networks. We transform the series of daily returns into complex networks, and analyze the local properties of these networks with respect to degree distributions, clustering, or average line length. We further use the clustering coefficients as quantities describing the local structure of the network, and approach them by using multifractal analysis. We find evidence of scale-free networks and multifractality of clustering coefficients.

Complex networks are a recent technique through which complex systems can be more deeply understood. The appeal of complex networks comes from the fact that they allow the study of different and complex systems in a way in which classical graph theory cannot be applied. The research so far has extended classical graph theory by developing statistical tools to study the topological properties of these complex networks at a local or global scale; see, for example, Albert and Barabasi [1], da Costa et al. [2], and Newman [3]. More recently, there has been a growing interest in approaching financial time series from the perspective of complex networks; see Refs. [4], [5], [6], [7] and [8]. In this paper, we propose the study of several key stock market indices from Central and Eastern Europe, namely the main stock market indices from the Czech Republic, Hungary, and Poland, in the context of complex networks. These markets have been studied not only less from the perspective of standard statistical and econometrical methods, as Bubak et al. [9] have noted, but also much less from the perspective of methods from econophysics. Notable exceptions are the papers by Jagric et al. [10] and Domino [11]. We derive complex networks from the series of daily returns of the selected stock market indices, and analyze the local properties of the resulting networks, such as degree distributions or clustering. Taking the clustering coefficients as measures, we further analyze them with respect to the presence of self-similarities.

The application of complex networks, although rapidly extending in many fields, has received limited attention within economic disciplines. In this study, we have examined several emerging European stock market indices through the use of complex networks. We found homogenous characteristics with respect to the statistics of complex networks. We also found close values for the exponents of the power-law distributions characterizing the degree distributions of the complex networks. The results also indicated the presence of scale-free characteristics of the complex networks. We finally extended the analysis through the use of multifractal analysis of the clustering coefficients, deriving multifractal spectra. We found evidence of self-similarity in the clustering coefficients.