金融数据挖掘中的非线性相关跟踪技术

摘要

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.%金融数据挖掘是信息社会中一个极具挑战性的研究方向.金融数据的随机特性使得隐藏在数据中的内在规则难以被发现.指出了经典相关分析的缺陷,进一步讨论了高阶相关系数的性质,证明了高阶相关不仅能描述隐藏的非线性相关信息,而且正好刻画了线性相关与独立之间的空白.因此,完全可以利用高阶相关性的计算简单性对金融数据中的时变非线性相关特性进行实时跟踪,克服了Brock W.等人于1987年和1992年提出的Granger-Causality独立性检验方法中需要正态假设和非实时性的缺点.最后,将上述结果应用于股票价格与成交量之间的相关分析.数值结果显示高阶相关能跟踪隐藏在数据中的时变非线性相关特性.