| After decades of rapid development since 1990,China's stock market has been continuously improving its status in the economy.The stock market provides investors with opportunities to benefit,enterprises with opportunities to expand their scale,and provides reference for the state to regulate the economic situation.Therefore,the study of stock market is of great significance to individuals,enterprises and countries.Shanghai stock market is an important part of China's stock market.The correlation study of Shanghai stock market is helpful to understand the law of China's stock market more comprehensively and objectively.Based on q-detrended correlation coefficient,random matrix theory and complex network theory,this paper proposes a theoretical method to study the correlation of time series,and empirically analyzes the correlation and evolution trend of the return series of 180 stocks in Shanghai Stock Exchange.The main work of this paper is as follows:(1)Based on q-detrended correlation coefficient and random matrix theory,the dynamic characteristics of the correlation matrix were explored,and the interval of the sudden change point of the data was determined by combining the least square regression.The specific time of the sudden change point was determined according to the actual trend and events of the stock,and the piecewise processing of the data was completed.The correlation between the stock return of SSE 180 was analyzed by using the sliding window technique and q-detrended correlation coefficient,and the phase space reconstruction method was used to determine the size and step size of the sliding window.Combined with the random matrix theory,the dynamic characteristics of the correlation coefficient matrix were investigated in two cases with or without overlap of sliding windows.By comparing the different order number q,stock average intensity,the eigenvalue and eigenvector,the results show that the bigger the order q is,the smaller the average strength is.The larger the order q is,the smaller the average correlation intensity is.The average correlation of the stock market dominated by large fluctuations is not as high as that of the stock market dominated by small fluctuations,but the trend of the correlation over time is consistent under different orders q.Finally,based on the least square regression,combining with the actual stock trend and the occurrence time of major economic and political events,the abrupt point of the stock market system is determined,and the evolution law of the stock market system in different periods is studied.(2)On the basis of the previous results of the system mutation point,the evolution law of SSE 180 stock market is explored.Based on the theory of complex network,this paper builds the network of 180 stocks in Shanghai Stock Exchange,ranks the stocks according to three kinds of centrality indexes,and analyzes the industry information of the stocks.Firstly,the correlation matrix sq C),(is calculated and the network is built according to the stock return sequence of each period after the period,and the industry information reflected by the correlation matrix structure under different order q is discussed.Secondly,the nodes in the network are sorted based on the centrality index,and the industry proportion and fluctuation reasons of the top ten stocks are also analyzed in combination with practical factors such as economic and political major events.Contrast analyzed under different values in different periods,scale s ranking,the mining industry situation of stock market in different period of evolution,to explore the change scale s got no stock is different,but generally the industry trend is the same.This paper presents a theoretical method to study the correlation of time series,which can be used to analyze the correlation of stock market data and help investors,enterprises and countries better grasp the evolution law and systemic risk of stock market.This method can also be used for correlation analysis of data in other fields. |
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