基于主成分分析的模糊时间序列研究

发布时间：2018-02-21 17:48

本文关键词： 主成分分析模糊协方差矩阵规则优化正定化　出处：《大连海事大学》2017年硕士论文　论文类型：学位论文

【摘要】：模糊时间序列模型是数据预测分析研究领域中一个广泛研究的课题,是为解决经典时间序列分析方法不能处理模糊类问题应运而生的。目前,模糊时间序列已被成功地应用于股指预测、入学人数预测、温度预测和航运指数预测等方面。为了进一步提高预测精度,学者提出了许多不同的模糊时间序列模型和预测方法,但其中多数方法都是围绕论域的划分和模糊规则的构建方法两方面做了不同程度的改进。在实际的预测过程中,模糊规则之间往往存在着相关性和冗余性,这不利于预测过程的简化和预测精度的提高。因此,去除模糊规则之间的相关性和冗余性成为目前亟待解决的问题。针对如何去除规则间的相关性和冗余性的问题,本文基于主成分分析提出了一种模糊时间序列规则优化算法。考虑到主成分分析只适用于协方差矩阵为正定的情况,本文从协方差矩阵正定和协方差矩阵非正定两种不同的情况分别对算法进行了阐述和验证。协方差矩阵正定时,首先构建数据之间的模糊关系形成模糊规则,并将模糊规则用矩阵的形式表示,即构建模糊关系矩阵;然后通过不同方法构建模糊关系矩阵的模糊协方差矩阵;其次对模糊协方差矩阵进行主成分分析,提取模糊规则的主成分进而优化模糊规则;最后根据优化的模糊规则对亚马逊股票的收盘价进行预测,验证了算法的有效性。协方差矩阵非正定时,首先对非正定的协方差矩阵进行正定化,得到一个近似的正定相关矩阵代替原始协方差矩阵。其它步骤均与协方差矩阵正定时相同,最后通过对Alabama大学的入学人数进行预测,验证了算法的有效性。本文将基于主成分分析的模糊时间序列优化算法的应用范围进行了拓展,不仅使得算法同样适用于协方差矩阵为非正定的情况,还提高了预测的精度;这充分说明新算法是有效的。
[Abstract]:Fuzzy time series model is a widely studied topic in the field of data prediction and analysis. Fuzzy time series have been successfully applied to the prediction of stock index, number of students, temperature and shipping index. In order to improve the prediction accuracy, many different fuzzy time series models and methods have been proposed. However, most of the methods are improved in different degrees around the division of the domain and the construction of fuzzy rules. In the actual prediction process, there is always correlation and redundancy between the fuzzy rules. This is not conducive to the simplification of prediction process and the improvement of prediction accuracy. Therefore, removing the correlation and redundancy between fuzzy rules is an urgent problem to be solved. In this paper, a fuzzy time series rule optimization algorithm based on principal component analysis (PCA) is proposed. In this paper, the algorithm is explained and verified from two different cases of covariance matrix positive definite and covariance matrix non-positive definite. When covariance matrix is positive definite, the fuzzy relation between data is first constructed to form fuzzy rules. The fuzzy rules are expressed in the form of matrix, that is, the fuzzy relation matrix is constructed, then the fuzzy covariance matrix of fuzzy relation matrix is constructed by different methods, and the principal component analysis of fuzzy covariance matrix is carried out. The main components of the fuzzy rules are extracted and the fuzzy rules are optimized. Finally, the closing price of Amazon stock is predicted according to the optimized fuzzy rules, and the validity of the algorithm is verified. When the covariance matrix is not positive definite, The nonpositive definite covariance matrix is transformed into positive definite matrix, and an approximate positive definite correlation matrix is obtained instead of the original covariance matrix. The other steps are the same as the positive timing of the covariance matrix. Finally, the number of students enrolled in Alabama University is predicted. The validity of the algorithm is verified. In this paper, the application scope of fuzzy time series optimization algorithm based on principal component analysis is extended, which not only makes the algorithm suitable for covariance matrix with non-positive definite, but also improves the precision of prediction. This fully shows that the new algorithm is effective.
【学位授予单位】：大连海事大学
【学位级别】：硕士
【学位授予年份】：2017
【分类号】：O159

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