Financial data mining is one of the most challenging research directions in information society. Financial data with random characteristics make it difficult to find out the rule hidden in data. In this paper, it is pointed out that correlation coefficient can not capture nonlinear information, which is the serious defect of classic correlation analysis. Furthermore, the properties of the high-order correlation coefficient are discussed, and it is proved that high-order correlation can not only describe the hidden nonlinear correlation, but also fill up the space between classic correlation and independence. The computational simplicity makes the high-order correlation coefficient be an effective technique to track nonlinear relation between variables. Finally, the above results are applied to the correlative analysis between stock price and stock trading volume, and the computing results show that the high-order correlation coefficient can track the time-varying nonlinear characteristics.