灰主成分分析研究及其应用

针对主成分分析方法对于具有时间序列数据的处理存在的不足,根据灰系统中数据具有时间序列的特性,将灰色系统思想与经典主成分分析相结合,提出一种新的模型,即灰主成分分析。时间序列分析不仅可以从数量上揭示某一现象的发展变化规律,还可从动态的角度刻画某一现象与其他现象之间的内在数量关系及其变化规律。灰色系统理论通过序列的生成和开发,致力于现实规律的探讨,而数理统计则致力于统计历史规律的研究。将两种方法的优点结合到一起,用于解决时间序列问题,并利用面向对象程序设计的方法进行了系统实现。将该方法应用到我国国债风险指标的综合评价中,突出了新的时间序列数据对整个数据的影响性,分析结果能够为决策者提供有价值的决策依据。实验结果表明,采用灰主成分分析的效果更优越,能较真实地反映出时间对于样本数据的影响。

Grey Principal Component Analysis and Its Application

In order to make up the deficiency that it can not solve the time series data,we propose a new method.Time series analysis can reflect the development of change order from the data,and also can depict the interior data relation and the change orderliness from a phenomenon to a phenomenon.Because the grey system data have time series characteristics,we combine the grey system method with the Principal Component Analysis,forming a new model,i.e.Grey principal component analysis.Grey system theory is devoted to the discussion of real order,while the mathematical statistics is devoted to counting the research of the historical orders.Therefore we combine the two methods to solve the time series.We use object-oriented programming method to implement the system,and based on correlation to make analysis separately.Finally,we apply this method to the synthesis appraisal of our national debt's risk,the result is remarkable,the new time data can affect the whole data of the system,and the result can help the manager make a decision.There is certain reference value to the research for the future in the time series'problem that this paper puts forward.