Analysis Of The Volatility Trend Characteristics Of The Shanghai Composite Index Based On The Complex Network Analysis Method

The stock price index is a comprehensive reflection of stock price fluctuations,so the research on the changes in stock prices has always attracted the wide attention of scholars and investors.The Shanghai composite index reflects the changes in the prices of listed stocks on the Shanghai Stock Exchange.A large number of industries,themes,styles,and strategies derived from the Shanghai composite index system provide more and more professional trading products and investment methods,which have improved market liquidity and effectiveness.Therefore,the Shanghai composite index has gradually become the core index of the market.Based on the complex network analysis methods,this study analyzed the regularity and characteristics of the volatility trend of the Shanghai composite index to explore the trend of stock prices.Firstly,we selected the time series of the closing price of the Shanghai composite index from January 7,2000,to November 20,2018,as the research object.We coarse-grained the time series according to fluctuations,established a coarse-grained complex network model and studied the basic topological structure properties of the network,including degree distribution,average path length,clustering coefficient,and betweenness centrality.The results showed that the degree distribution of the network approximately obeyed the power-law distribution,that is,it conformed to the characteristics of scale-free networks.The average path length between the mode nodes in the network was short,and the shortest path length distribution approximated a bell-shaped distribution,in which the shortest path value of 6-10 was the majority.These results indicated that the network mode nodes switched more frequently.The clustering coefficient of only a few nodes in the network was not zero,which indicated that the network was not closely connected and the nodes were relatively scattered.Besides,the mode nodes with a large betweenness centrality and the mode nodes in the k4 core played important roles in transition in the network.Also,the regularity of the emergence of new mode nodes showed that the total number of nodes increased linearly with the cumulative time,providing a basis for predicting the time of the emergence of new mode nodes in the future.Secondly,according to the fluctuation of the time series of the Shanghai composite index,we studied the periodical network model over time to explore the characteristics of the network.The results showed that the node type,node strength,average path length,network diameter,and node with a large betweenness centrality at different times changed over time.With the change of time,the node type showed fluctuation growth,the average node strength fluctuation decreased,the average path length and the network diameter showed fluctuation growth,and the nodes with larger betweenness centrality changed from mainly consisting of gentle rise and gentle decline to gentle rise,gentle decline,sharp rise,and sharp decline.The network develops towards the direction of diversification,sparse and complexity.Finally,in the research of the prediction model algorithm,we applied the conversion frequency of a mode node to another one to calculate the frequency of the transition and used it as the probability of conversion between the mode nodes.