Complexity

Volume 2017 (2017), Article ID 4370203, 11 pages

https://doi.org/10.1155/2017/4370203

## Dynamic Evolution of Securities Market Network Structure under Acute Fluctuation Circumstances

^{1}School of Management and Engineering, Nanjing University, Nanjing 210093, China^{2}School of Economic and Management, Nanjing Tech University, Nanjing 211816, China

Correspondence should be addressed to Tingqiang Chen

Received 2 June 2017; Revised 27 August 2017; Accepted 14 September 2017; Published 6 November 2017

Academic Editor: Dimitri Volchenkov

Copyright © 2017 Haifei Liu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

This empirical research applies cointegration in the traditional measurement method first to build directed weighted networks in the context of stock market. Then, this method is used to design the indicators and the value simulation for measuring network fluctuation and studying the dynamic evolution mechanism of stock market transaction networks as affected by price fluctuations. Finally, the topological structure and robustness of the network are evaluated. The results show that network structure stability is strong in the bull market stage and weak in the bear market stage. And the convergence rate of the dynamic evolution of network fluctuation is higher in the bull market stage than in the bear market stage.

#### 1. Introduction

In the financial market, individual and institutional investors, listed companies, and trading systems have self-organizing characteristics. Mutual relationships between investors, investment banks and financial analysts, investment funds and listed companies, and so forth form the network topological structure of financial securities market. Network structure plays an important role in information transmission and risk contagion. The higher the network concentration of securities, the higher the volatility of securities. Moreover, network structure influences the learning mechanisms of investors. That is, investors often use different aspects of their social networks to update investment beliefs and make decisions. In addition, network structure has a certain influence on the decision-making and corporate governance of listed companies. Network structure can be used to reflect capital market volatility and stability. Therefore, depicting the network structure of securities fluctuation is a feasible way of analyzing the influence of random factors on the macro behavior of the financial market.

Network structure has been applied in the financial market via the complex network theory and method. But network structure cannot give play to the advantages of traditional research methods, and it is difficult to analyze and measure the fluctuation of economics using the simple network analysis methods. Therefore, the current study employs cointegration in the traditional measurement method to build a directed weighted network of the stock market and design the indicator and the value simulation for measuring the fluctuation of this network. We aim to study the dynamic evolution mechanism of the stock market transaction network in a state of fluctuation and thereby evaluate the topological structure and robustness of the network. The methods used in this paper have been researched and empirically tested in the Shanghai–Hong Kong Stock Connect market and defined by different time windows.

The remainder of this paper is structured as follows. Section 2 provides a review of and commentary on previous, relevant literature. Section 3 describes the research method and model building and expounds on the specific methods used for the analysis of stock market stability. Section 4 presents the empirical analysis based on sample stocks from the Shanghai–Hong Kong Stock Connect market. Section 5 provides the research conclusions.

#### 2. Related Literatures

With the continued development of the financial sector, the ties among market entities have become closer in terms of breadth and depth and have formed a complex system. Benefitting from the introduction and deepening of the complex network theory, the complex financial system method can best be described through comparison with traditional measurement methods. The internal structure of financial systems posits that while the latter may not always be stable, they can be relatively stable over a longer period. Financial and social networks have similar degrees of distribution and small world effects. Using the social network analysis method can thus help develop a new recognition of the relationship between nodes in the financial network (government, institutions, and individuals) and provide guidance to the regulation of financial reform and financial risk [1, 2]. To date, studies on complex finance networks have mainly involved their description, as well as the analysis of their stability and degree to which they could carry the contagion of financial risk.

In describing financial networks, researchers have built network structure and explored the nature of the network statistics of different financial institutions [3–7], stock markets [8–10], international stock markets [11], crude oil future and spot markets [12], open-end fund markets [13], and mutual fund markets [14]. For example, Huang et al. [15] constructed a financial network of China’s SH 180 Index and SZ 100 Index constituent stocks and explored the correlations among the stocks. Most descriptions and analyses of stock transaction networks indicate that the tail-end of the degree distribution of stock transaction networks has the characteristics of the power-law distribution [16]. Wang [17] constructed a weighted stock network by taking the second-board market in China’s Shanghai securities market as the data source and researching the stock network’s “rich group” coefficient. He found the clear existence of such a “rich group” by exploring the random network with the same distribution degree.

Some works used the complex network theory to investigate the contagion of global financial system (Kali et al., 2009; Gai and Kapadia, 2010; Chen et al., 2016) [2, 18, 19], established a network model for the global transactions system, and studied global communications with regard to financial crises by measuring the indicators of network correlation and centrality among others [4, 19, 20]. To study the interactive influence mechanism among interfinance risk, some works established a financial network model that enabled them to analyze the robustness of a financial system on the basis of the complex network theory (Gai and Kapadia, 2010) [19], and analyzed the common characteristics of the optimal financial network and the topological structure of actual financial networks [19]. Some scholars further studied the behavior of a network structure in financial contagion and proposed relevant measures to improve the stability of a financial system from the financial network angle by preparing policy guidance for preventing crisis-level contagion [2, 4, 7, 19] (Wu et al., 2014; Chen et al., 2016). For example, Winecoff [21] studied the influence of global financial crises on politics and economics from a macro angle by establishing a complex network model. In addition, some works studied the stability of financial network. For example, Tumminello et al. [22] employed the MST and PMFG algorithms to build a complex network of 300 stocks from the New York Stock Exchange and found that the lower the data frequency, the more prominent the network hierarchy is. Huang et al. [23] used a threshold method to construct the financial network structure of China’s stock market by analyzing the nature and topological stability and studying the topological robustness of the network and found that while the financial network had certain robustness against a random attack, it was brittle against a calculated attack. Lin et al. [24] employed MST and PMFG to build and analyze a financial market network by dynamically highlighting the key node in the network, studied the network stability, and certified that it is robust in terms of recognizing the key node using the centrality of the complex network node. Vitali et al. [25] dynamically analyzed the relationship between network nodes by establishing a financial network model between banks and companies, analyzing the indicators of the network’s topological structure, and studying the network’s degree of invulnerability. Our aims are to integrate the econometrics model with the building of a complex financial market network and design relevant indicators to weigh the robustness of this network dynamically.

#### 3. Research Method and Model Building

##### 3.1. Building a Directed Weighted Network

The linear combination of two or more nonstationary time series may be of stationary or low-order integration. In an actual financial market, certain time series that are not stationary exist and may cause inconvenience in the analysis, but others are stationary (equal-average, finite variance, and autocorrelation coefficient is the function of lag intervals for endogenous) and follow the linear combination. From a financial perspective, when different nonstationary time series turn into stationary ones following a linear combination, equilibrium exists between these series. The relationship, which is known as cointegration, is stable on a long-term basis. In financial measurement, cointegration can describe the stable long-term relationship between two or more series. Therefore, this paper proposes building a directed weighted network based on the cointegration between stock time series.

Generally, to test the cointegration of two time series, we use the Engle–Granger two-step method based on Yang et al. [26] and Tu [27]. Suppose and are the logarithm return series of two stocks, wherewhere denotes the restoration of the right price of stock at time and denotes the restoration of the right price of stock at time .

Then, the cointegration test of and should be performed by supposing the equation where represents intercept term of the above long-term cointegration equation, is defined as regression coefficient, and is disequilibrium error.

If the number of stocks is , two-two stock pairs can be formed completely by . In this case, the cointegration test should be performed times to determine whether a connection exists between the two stocks. If a stock pair fails to pass the cointegration test, then the relationship that exists between the two stocks is not stable and a corresponding connection exists.

For every group of stock pairs that pass the cointegration test, we build an error correction model and use the first-order lag series to judge the causality and determine the direction of the connection. The regression coefficient obtained from the equation serves as the weight of the side.

If in (3) is significant but in (4) is insignificant, the logarithm return of stock will influence the logarithm return of stock . Meanwhile, the logarithm return of stock will have no influence on the logarithm return of stock . Hence, the directions of Nodes and in the network structure are such that Node points to Node , and the weight is . If in (3) and in (4) are significant, then a relationship of mutual influence exists between the logarithm return of stock and the logarithm return of stock . In the network, Nodes and are bidirectional, and their weights are and , respectively.

The weight of edge of the network constitutes the network’s connection matrix (). If , Node does not point to Node . The in- and out-strength of every node are then calculated usingwhere refers to the weight that Node points to Node , means that is close to and points to the Node set, and means that Node is close to and points to the Node set.

Given nodes with maximum strength and allowing for a certain degree of fluctuation in each node, the fluctuation of every spreads along the side of the network. Studying the fluctuation of the whole network over time enables the evaluation of the stability of the whole network.

##### 3.2. Analysis Matrix of Network Stability

Supposing that the stock returns of all nodes in the network are at time 0, and creating a certain disturbance in the network node at a certain time that yields , the range of variation of will be due to the price limits in China’s stock market. To explore the influence of on network node yield at Moment 1, we define the first-order effect matrix as follows:

The first-order effect matrix refers to the first-order lag effect weight if the yield of has no influence on the yield of when . Under other circumstances, when has influence over . If is irrelevant to .

Supposing there is an influence of every stock node on the other stock nodes in the network, then the relationship can be superimposed in a linear manner, as expressed by the following equation:

If changed into the matrix format, then the relationship takes the following form:

To study the dynamic evolution characteristics of the network yield disturbance at time 0 over time, this study designed the measurement indicator based on the weight-related matrix. where refers to the arithmetic mean of . Indicator rejects spontaneous change over the time of the yield of the stock node. The result could only explore the influence of the network’s yield disturbance at time 0 on the yield of the entire network through network-based communication.

#### 4. Empirical Research and Analysis

##### 4.1. Data Source and Variable Selection

The China Securities Regulatory Commission and the Securities and Futures Commission of Hong Kong jointly issued a proclamation on April 10, 2014. On November 17, 2014, the transaction was officially opened. This study obtained data of 884 stocks from the WIND database as the initial sample, which consisted of 568 Shanghai-to-Hong Kong and 316 Hong Kong-to-Shanghai trading stocks. The sample series duration taken was November 17, 2014, to January 27, 2016. During this period, the Shanghai Composite Index reached 5,178 on June 12, 2015, but later fell steeply and decreased to 2,638 on January 27, 2016. We then divided the time window of the sample series into two sections. The first section was from November 17, 2014, to June 12, 2015, and was referred to as the “pre-stock market disaster period.” The second section was from 12th June 2015 to 2nd January, 2016, and was referred to as the “post-stock market disaster period.” After rejecting the 44 stocks listed later and in suspension, the remaining 840 stocks were used as the final sample (Figure 1).