Correlations Of Stock Markets

Time series analysis is a statistics method of dynamic data processing, becoming an integral part of the financial market, especially the research of stock market. It is a important method for qualitative and quantitative research of stocks. Many research achievements of financial markets are raised based on the basis of time series analysis, which has been widely recognized in the world.In this paper, we study three time series complexity methods, namely Asymmetry detrended cross-correlation analysis (A-DCCA) method, Detrended cross-correlation analysis coefficients (DCCA coefficients), Information categorization. These three methods are used to investigate Asymmetry cross-correlations, multi-scale cross-correlations and similarities between the two series, respectively.A-DCCA method combines the DCCA and asymmetric DFA methods, obtaining the asymmetry cross-correlation coefficients by fitting. This method is used to analyze the asymmetry of wave functions when time series have positive or negative trends. Compared to traditional methods, this method provides more abundant cross-correlation information, and then we put forward A-DCCA method based on local scale to study the properties of the local scaling A-DCCA method. DCCA coefficients method is mainly used for detection cross-correlations of non-stationary time series, combining the Detrended fluctuation analysis (DFA) and DCCA methods. This method use a new correlation coefficient to define the cross-correlations of two series, expanding multiple scales from the previous single scale, thus proceeding a more comprehensive analysis. Information categorization method can quantize the similarities between the symbol sequences mapping from time sequences. The using of Shannon entropy as weights can make the results more meaningful.There is a positive relationship between the stock market and the real economy. The stock index acts as a barometer of the economy, reflecting the operating state of the economy, which making our studies more important. We selected six representative stock indices, and are divided into two groups. One group includes three western stocks, which are S&P500indices of America, FTSE100indices of England and DAX indices of German. The other includes three Chinese stocks, which are the Shanghai Composite (Shang Zheng), Compositional Index of Shenzhen Stock Market (Shen Cheng Index) and the Heng Sheng Index. The above three methods are used to analyze the complexity of the six stocks, and explore the change of time complexity before, in and after global financial crisis. The obvious differences have been discovered between western and Chinese stock market. On the whole, when China’s stock index increases, there are stronger cross-correlations between the rests. China’s stock markets have a stronger cross-correlation than western stock markets. The Shang Zheng index, Shen Cheng index have stronger similarities than others. In particular, although belong to China’s stock index, but the Hang Seng index has a bigger difference on the asymmetry, cross-correlation or similarity between the Shang Zheng index, Shen Cheng index. The asymmetry, cross-correlation and similarity of the stock indices are obviously different in three periods of the financial crisis. The cross-correlations and similarities of three Chinese stocks become stronger after the global financial crisis. The paper contains18figures,9tables,51references.