Research on the evolution of stock correlation based on maximal spanning trees

In this study, we choose the daily closing price of 268 constituent stocks of the S&P 500 index, 221 stocks of London Stock Exchange, 148 constituent stocks of the Shanghai Composite index and 152 constituent stocks of the Hang Seng index as the research objects and select the sample of all the stock markets from 2 January, 2003, to 16 September, 2013. For each stock market, first, using a moving window to scan through every stock return series and mutual information to measure the statistical interdependence between stock returns, we construct a corresponding weighted network in every given window. Then we study the evolution of stock correlation by analyzing the average mutual information, mutual information distribution and topology structure's variation of the maximal spanning tree extracting from every weighted network. All the obtained results indicate that for all the stock markets, both the average mutual information and the standard deviation of mutual information distribution first gradually increase and they reach a peak during the full-outbreak periods, and finally, they decrease again. In addition, the topology structure of the maximal spanning tree also changes from compact star-like to loose chain-like first and then turns to compact star-like once more. All the facts tell us that the crisis does change the stock correlation and the stock correlation is from weak to strong first, and then becomes weak again.