【作者】 姜春燕；

【导师】 林和平；

【作者基本信息】 东北师范大学 ， 计算机软件与理论， 2008， 硕士

【摘要】 在经济、金融、控制和决策等许多领域,经常要对大量统计数据进行实时处理,但近年来,伴随大量多指标时间序列数据的出现,对统计方法的准确性、可靠性又提出了更高的要求。常用处理多指标数据的方法是主成分分析法。但是,该方法不能反映具有时间序列数据的变化特征与趋势,无法提供正确的决策支持。而灰色系统理论的研究主要是基于时间序列累加,强调新息优化,研究现实规律。本文在主成分分析法的基础上,结合灰色理论累加的思想,提出新的方法,灰主成分分析方法,用于解决多指标时间序列的综合评价问题,弥补主成分分析方法的不足,并且得到很好的效果。本文主要研究内容和取得的成果如下:1.深入研究综合评价方法、主成分分析方法现状,对当前的方法进行了概括和总结,在做大量实验的基础上,发现其缺点。2.根据其缺点,查找书籍与相关文献资料发现灰色系统理论适合于解决时间序列的问题,因此,在深入研究灰色系统理论的基础上,根据灰度和累加的思想重新定义了主成分分析方法中的基本统计特征:均值、方差、协方差以及相关系数。3.给出灰主成分分析方法的基本思想、步骤、算法流程以及仿真实例,仿真实例中采用不同的方法进行对比分析,以证明本文提出方法的有效性,分析结果更加合理、准确。该方法具有以下优点:一方面减少了指标个数,简化了分析问题的难度;另一方面可以及时、准确地反映基于时间序列数据的变化特征与趋势,能够根据动态数据揭示系统动态结构和规律,尽可能多的从中提取出需要的准确信息,以便对系统的未来提供决策支持。4.以本文提出的算法为基础,利用Microsoft Visual C++.Net开发工具设计并实现了一个基于Windows操作系统的灰主成分分析的计算平台。5.采用两个不同的实例作为测试数据对算法进行测试,使用不同的方法进行对比分析,结果表明本文的方法在处理多指标时间序列数据方面是有效的,分析结果能够为决策者提供有价值的、正确的决策依据。该方法对统计学在多指标时间序列的问题研究中起到了推动作用。更多还原

【Abstract】 The large quantities of statistical data often need be processed real-timely in many fields, for example the economy, finance, control and decision-making, but in recent years, with the emergence of the large number of multiple indicators time-series data, which puts forward higher requirements for accuracy and reliability of the statistical methods. Principal component analysis is often used to deal the multiple indicators data. But the method can’t timely and accurately reflect the change characters and the trends of the time series, and can’t supply the right decision-making. However, the study of the grey system theory mainly bases on the cumulative time series, which emphasizes the new data optimization and researches on real regulation.This paper is on the basis of principal component analysis method, combining with the cumulative thinking of grey theory. We put forward a new method, which is grey principal component analysis method for solving the comprehensive evaluation problems of multiple indicators time series data to make up the principal component analysis’deficiencies. The studies and the results of this paper obtained are as follows:1. We have studied on comprehensive evaluation methods and principal component analysis deeply, summarized the current methods. We find its disadvantages on the basis of doing a lot of experiments.2. According to its disadvantages, searching the related books and literatures to find that the grey system theory is fit for solving the issues of the time series, therefore, according to the grey degree and cumulative thinking, this paper redefines the basic statistical characteristics of the principal component analysis: mean and variance, covariance and correlation coefficient.3. This paper presents the basic idea, steps, the algorithm processes of the grey principal component analysis method, and gives the simulation examples, which uses the different methods to analysis the data, so that can prove the effectiveness of the method we propose in this paper, the result of the analysis is more rational and accurate; On the other hand, the method can timely, accurately reflect the change characters and the trends of the time series, revealing the dynamic structure and the regulation of the systems according to the dynamic data. It can extract the accurate information that our needs as much as possible, so that can supply the decision support for the future.4. On the basis of the algorithm this paper proposes, we use Microsoft Visual C + +. Net development tools to design and implement the grey principal component analysis computing platform basing on windows. 5. Using two different examples as test data to test the algorithm, comparing with the different methods, the results show that this method in dealing with the multiple indicators time series data is more effective, which can provide the valuable, accurate decision-making. The results of the experiments show that the grey principal component analysis method which this paper puts forward plays the important role in the statistical indicators time series data problems and has the effects for the future research.更多还原