Directed Cross-Correlation Research Between Stocks Based On Complex Network

With the global economic integration, economic exchanges and cooperation between countries and regions will be more frequent, and the international economic situation develops towards a new pattern. The security of national economy will be more prominent, the investment guidance to the development of industrial economy becomes more important, and the risk management difficulty to securities investment has also increased. Under the influence of these factors, it has more importantly theoretical and practical significance to the research on the directed cross-correlation of countries, and also the enterprise within regions and industries.Society economy system is a complex system. There are also a lot of complex systems in the nature and human society. With the progress of scientific research and the improvement of human knowledge, the new progress of complex system research has been obtained. It is easy to see that the complex network method has been used for so many complex systems research. However, not only for the economy and finance complex systems, but also for the other complex systems, there is little research about directed cross-correlation between different elements within the complex systems. In this paper, the stocks in Chinese stock market and the stock market indexes in different countries have been studied. According to the cross-correlation fluctuation of stock prices and stock market indexes, using the data mining, quantity statistics, empirical analysis methods, we build a directed complex network model in the stock market. Moreover, based on the stock price per minute transaction data, the directed complex network model has been verified, it is also proved that the directed complex network existed in Chinese stock market. At the same time, the directed complex network of china rock market has been constructed. Meanwhile, we take some of stocks as an example, and give the directed complex network graph. Finally, by comparing the undirected complex network in stock market, we define the structure properties of directed stock market complex network. Furthermore, the structure properties of directed network in Chinese stock market has been analyzed, it is obtained that most stocks has stronger self-correlation, but there are no more stocks with obvious cross-correlations in Chinese stock market. In addition, the out-degree distribution and the in-degree distribution of nodes in Chinese stock market network follow the power-law model.Based on the directed complex network model in stock market, the following research content summarized below.1. According to the directed cross-correlation coefficients of stocks calculated in the process of the directed complex network model constructing, the moving trends of stock price and the range of it has been predicted in Shanghai A-share stock market, and the every minute prediction result and real exchange data of stock prices has also been compared and analysed.2. In view of the imbalance of Chinese regional economic development, in order to invest and guide the regional industrial economy scientifically and reasonably, adjust and upgrade the industry structure, and develop the regional economy harmoniously, healthily, rapidly and sustainably, in this paper, we study the directed cross-correlation between stocks and corresponding listed companies in regional blocks, and also study the relationship between the cross-correlation of stocks and the one of entity economy. Meanwhile, combining with the imbalanced actuality of Chinese regional economic development, we study stocks clearly in Xinjiang and Inner Mongolia regional blocks since there is remote location, abundant natural resource and good potential of economic development, and make the comparative analysis about the stocks and enterprise economics in Xinjiang province.3. Considering the importance of industry economics in the whole national economy, as well as the importance of industry factors in the process of stock market investment analysis, first, according to "national economy industry classification and code","guidance on the industry classification of listed companies" announced by the China Securities Regulatory Commission in2001April, and the standard of industry classification on listed companies divided again by CITIC Securities companies, we present the industry classification in the paper. Second, using the directed complex network model, the directed cross-correlation of stocks in Chinese industry blocks is studied. Third, we select coal block and financial block randomly from fifty industry blocks divided above, analyse the directed cross-correlation of stocks within the blocks in detail, and make the comparative analysis about the stocks and enterprise economics in coal block. And then, the comparative analysis about the industry block and regional block is made from the perspective of reference value on securities investment.4. We realize the cross-correlation between different countries’financial markets in the process of financial globalization, and take the stock market indexes in different countries as independent nodes. First, we choose eight stock market indexes as German DAX30index, Britain’s FTSE100index, Dow Jones Industrial Average index, NASDAQ Industrial Average index, France CAC40index, Hang Seng index, Nikkei225index and Shangzheng index, and use the directed cross-correlation calculation model of the stock market indexes to analyze the directed cross-correlation of the indexes. And then, the long time range and short time range directed cross-correlation among Dow Jones Industrial Average index, NASDAQ Industrial Average index and Shangzheng index are especially studied.For the above research, the following corresponding conclusions are obtained.1. It is found that most stocks have the same fluctuation trend between prediction result and real trading data except for the two time intervals as10minutes after opening and8minutes before closing in every trading day. After the two abnormal time intervals is removed and the prediction value is rounded by0.01yuan, the average accuracy rate of price prediction will be improved.2. The directed cross-correlation of stocks in regional blocks does exist in Chinese stock market, and the trength of associated driven relationship between stocks and corresponding listed companies are defferent. By comparing and analyzing the relationship of the stocks and enterprise economics in Xinjiang province, it is showed that the driving strength of stocks in regional blocks is consistent with the total profit of the corresponding listed companies in entity economy.3. In the coal industry block and financial industry block, there are few stocks which can make other stock prices fluctuation with their own prices change; the differences between the cross-correlation coefficients for most stocks are not obvious, the cross-correlation of stocks seems uniform. By comparing the stocks and corresponding listed companies in coal block, it is found that the stock stronger driving, the more total profit of the corresponding listed companie in entity economy is, it is more important in the industry block. In addition, from the perspective of reference value on securities investment, industrial factors are more sensitive than regional factors; the cross-correlation n industrial block is stronger than that in regional block, so the industrial factors are more important than regional factors in stock selection, risk management and the portfolio of investment.4. In view of the cross-correlation of eight stock market indexes, the Dow Jones Industrial Average index has the strongest driving effect, and then NASDAQ Industrial Average index. The Nikkei225index is the easiest one affected by other stock indexes, in turn, are the Hang Seng index and Chinese Shangzheng index. In general, the stock index which has stronger driving effect is not easy to be influenced, but it is not the completely inverted relationship. Considering especially the Chinese and American stock market indexes, in long time range, the driving effect of Shangzheng index to the Dow Jones Industrial Average index and the NASDAQ Industrial Average index is very weak, conversely, their driving effects to Shangzheng index are quite strong; in short time range, it is found that the driving effect of the Dow Jones Industrial Average index and the NASDAQ Industrial Average index to Shangzheng index is becoming more and more strong, at the same time, the driving effect of Shangzheng index to the Dow Jones Industrial Average index and the NASDAQ Industrial Average index does exist in some time range, and it becomes obvious in the recent time range of September4,2009and March30,2012.