关键词: 多元统计分析, 单变量时间序列, 主成分分析, 聚类分析

Abstract: For the high dimensionality of time series, based on theoretical analysis, a new method is proposed to reduce the dimension of univariate time series via principal component analysis, thus univariate time series clustering method based on principal component analysis is presented. The main idea is that, similarities among the univariate time series are reflected by similarities among the corresponding coefficients under the same basic vectors of linear space. In the process of theoretical analysis, we firstly do the principal component analysis on univariate time series data sets and then analyze the relationship among univariate time series, eigenvectors of sample covariance matrix and principal components. Moreover, we prove that the vectors composed of principal components are linear independent. In order to further verify the correctness of theoretical analysis results and the performance of the proposed algorithm, simulation data and real stock data are used to do the numerical experiments finally.

Key words: univariate time series, principal component analysis, cluster analysis