مطالعه برهم انباشتگی شبکه های مالی در بازار سهام چینی

We propose a method based on cointegration instead of correlation to construct financial complex network in Chinese stock market. The network is obtained starting from the matrix of pp-value calculated by Engle–Granger cointegration test between all pairs of stocks. Then some tools for filtering information in complex network are implemented to prune the complete graph described by the above matrix, such as setting a level of statistical significance as a threshold and Planar Maximally Filtered Graph. We also calculate Partial Correlation Planar Graph of these stocks to compare the above networks. Last, we analyze these directed, weighted and non-symmetric networks by using standard methods of network analysis, including degree centrality, PageRank, HITS, local clustering coefficient, KK-shell and strongly and weakly connected components. The results shed a new light on the underlying mechanisms and driving forces in a financial market and deepen our understanding of financial complex network.

The financial market is a highly complex evolving system [1] and [2], still controversial [3], difficult to grasp and predict [1], and sensitive to economic instabilities, such as the Black Monday of October 19, 1987 [4], financial crisis of 2007–2008 caused by the subprime mortgage loan crisis [5]. So the study of it has rapidly been attracting interest within not only economics, but also mathematics and physics [2], [6], [7], [8] and [9]. Recently complex network (directed or undirected, weighted or unweighted) is found useful to characterize and better understand the financial market [1], [10], [11] and [12], in which each stock indicates a vertex and each interaction by a pair of stocks indicates a weighted edge that encodes the distance between them. But how to quantify a distance between different stocks traded in the financial markets and then construct a network to exact useful information is still a difficult and an open problem. Mantegna [13] was possibly the first to study financial markets in the concept of networks, who encodes the distance between two stocks as a function of Pearson correlation coefficient to construct the complete graph, and then implements filtering technique Minimum Spanning Tree (MST) to simplify and extract useful information from them, such as detecting a taxonomy that organizes stocks according to their economic activity. After this seminal work, many relevant papers emerge. Bonanno et al. employed the same methodology to find a meaningful taxonomy existing in stock market indices located all over the world [14], and high-frequency cross-correlation existing between pairs of stocks in US equity markets [15]. By observing the networks obtained from real and considered artificial markets, topology of the MST of them is different was found [16]. During a stock market crisis such as Black Monday, the tree length shrinks and strong reconfiguration take place [4]. Onnela et al. investigated another network, generally called asset graph, obtained by selecting only the N−1N−1 edges with lower correlation coefficient weights of the complete graph [17]. The construction of the asset graph was analyzed in Ref. [18], where the temporal evolution of the clustering and information was measured. Constructing networks from financial data also use threshold of correlations of stocks [19], [20], [21] and [22]. A complete analysis was investigated by Ref. [19], where repeatedly remove correlation links from lower to higher values or vice versa, and found that the low correlation links of the network contribute to the overall connectivity significantly more than the high correlation links. Encoding the distance between two stocks as a function of the correlation coefficient to construct the complete network has generally been used in financial theory and practice to quantify the degree of similarity among the stocks. However, correlation time series are just demanded to move in the same direction while the magnitude of the move is unknown, so academics have long since questioned that apply correlation to represent relationships between time series. On the other hand, since these networks are usually complete graphs (all links between vertices are present), how to extract useful information and understand the behavior of them are difficult. It has not been fully investigated and only a few methods have been developed until now, such as Minimum Spanning Tree (MST) [13], also called Asset Tree, Asset Graph [17], and Planar Maximally Filtered Graph (PMFG) [23]. In this paper we firstly apply Engle–Granger cointegration test between all pairs of stocks instead of traditional correlation to construct a non-symmetric matrix of cointegration pp-values. Then some tools for filtering information in complex network are implemented to prune the complete network described by the above matrix, such as setting a level of statistical significance as a threshold and Planar Maximally Filtered Graph (PMFG). To compare the above networks with network obtained by using other method, we also calculate Partial Correlation Planar Graph (PCPG) of these stocks. Last, we analyze these directed, weighted and non-symmetric networks by using standard methods of network analysis, including degree centrality, PageRank, HITS, local clustering coefficient, KK-shell and strongly and weakly connected components. This paper is organized as follows: Section 2 explains the data and methods used to empirically investigate. Next, Section 3 presents the results observed in accordance with the empirical design. Section 4 gives the advantage based on cointegration instead of correlation to construct financial complex network, the drawback of Engle–Granger cointegration test and the possibly next step research. Finally, the paper will be concluded in Section 5.

In summary, we apply the Engle–Granger cointegration test between all pairs of stocks instead of traditional correlation to construct a non-symmetric matrix of cointegration pp-values. Then some tools such as setting the level of statistical significance as a threshold and PMFG are implemented to form CITN and CIPG. Additionally, PCPG is calculated to compare the above networks. Last, we analyze these directed, weighted and non-symmetric networks by using standard methods of network analysis, including degree centrality, PageRank, HITS, local clustering coefficient, KK-shell and strongly and weakly connected components. We find that the CIPG and PCPG have similar properties such as scale-free, highest relative influence of sector 6 Financials, but CIPG is better to represent these properties than PCPG in this paper. Due to the mean degree of CITN is large, their properties approximate to corresponding complete graph. We also find some interesting results in volume of stocks by performing the same method and analysis. Some possible experimental research is currently under our investigation and will be reported elsewhere.