Characterization Of Price Return And Volatility Time Series By Complex Networks

Since the1990s, in the context of big data, the disciplines of complexnetwork had appeared and arrived at certain level along with the growth ofcomputer science and graph theory science. So far, there have been manyresearches on the theory of financial complex network, most of them discussedsomething about financial crisis caused by American subprime mortgage crisis.The main points of these studies almost focus on the change of structure roundabout the overall market financial crisis. There is not enough description onlong-time and large-scale stock portfolio in trading market. In the meanwhile,the analysis on statistical characteristic of complex network is less and less.In this article, the superiority of complex network theory is showed throughmodeling the stock price return time series and price volatility time series of theminimum spanning tree network. The main work of this article are analyzing thedistribution of nodes in the complex networks, giving advice about stockportfolio, describing the basic statistical characteristic of the complex networks,and discussing the stability of complex networks topological structure betweennetwork of price return and price volatility. Specific content as follows, firstly,setting up the network model by the actual stock prices selected. The Kruskalalgorithm of the minimum spanning tree is used to network formation of stockprice return and price volatility. Then we make the same analysis of the twovariables in statistical theory, so that we can point out the superiority ofcomplex network. In the next part of the article, it will summarize thecharacteristic of the stock industry concentration in complex networks throughthe detail description about the distribution of the nodes in the networks. In thesame time, some calculation will be needed to analyze the leading business oftrading market, and then it can offer help to the portfolio. And then, the keypoint of the last part in my article is the analysis of the statistical characteristic sof complex networks. We can get that the networks of price return and pricevolatility have both small world and scale-free features through obtaining thenumber of Hub nodes in the minimum spanning tree, calculating the statisticalcharacteristics of complex networks, such as distribution of network degree and average path length. At last, through the comparison according to the K-meanclustering analysis of network community structure, we can find the structuraldifferences between the minimum spanning tree of price return and pricevolatility.As the portfolio in actual market will be related with "Epps effect", there isalso something to talk about, that if the stock price return would be influencedby "Epps effect", with the change of the time interval. The answer has got tobe-in the article; we choose the price return of80stocks to set up the minimumspanning tree in different time interval. The results indicated that thedistribution of nodes in these minimum spanning trees has discrepancy, and th enconfirms the Epps effect in the minimum spanning tree.In this paper, We focus on making the financial time series into complexnetworks by the specific modeling and realizing the statistical characteristicsand topology structure analyzes about complex network. It has a high value ofpractical application and important significance in the stock trading marketportfolio.