一种融合模糊时间序列分析的成分数据时间序列预测方法  

method of compositional data time series prediction integrating fuzzy time series analysis

作　　者：陶志富[1,2,3] 谭文发 陈华友[1] TAO Zhifu;TAN Wenfa;CHEN Huayou(School of Big Data and Statistics,Anhui University,Hefei 230601,China;Center for Data Fusion and Development Applications,Anhui University,Hefei 230601,China;Research Center for Applied Mathematics Research,Anhui University,Hefei 230601,China)

机构地区：[1]安徽大学大数据与统计学院,合肥230601 [2]安徽大学数据融合与开发应用中心,合肥230601 [3]安徽大学应用数学研究中心,合肥230601

出　　处：《系统工程理论与实践》2023年第5期1534-1544,共11页Systems Engineering-Theory & Practice

基　　金：安徽省自然科学基金(2108085MG239);教育部人文社科研究目规划基金(21YJCZH148);安徽生态与经济发展研究中心2021年度教师课题(AHST2021002);国家自然科学基金(71871001)。

摘　　要：在诸多社会和经济问题中,成分数据由于可以提供整体视角下各部分的比例情况而备受关注.对数比变换和球坐标变换等变换方法为成分数据时间序列的专业预测提供了可能,但两类变换均对成分数据的分量进行了限定性要求,如不能包含0或者1.因而,在理论上探求新的成分数据时间序列预处理方式或预测模式具有重要意义.通过将模糊时间序列分析与成分数据时间序列预测相结合,本文提出一类融合模糊时间序列分析的成分数据时间序列预测方法.首先,利用信息熵测度,将成分数据时间序列对应到实值序列框架下.继而,在模糊时序分析框架中,利用模糊C均值聚类实现成分数据时间序列对应实值序列论域的划分并建立模糊集与成分数据之间的对应关系.进而应用一阶模糊时间序列分析模型实现对成分数据时间序列的预测.最后,通过某汽车公司的汽车销售结构数据实证分析验证了所提出预测方法的有效性.In many social and economic problems,compositional data has attracted much attention because it can provide a holistic view of the proportion corresponding to each component.Up until now,the introduction of logarithmic ratio transformation and spherical coordinate transformation makes it possible to realize professional predictions of compositional data time series.However,some preconditions about the components are required in the two types of transformations,such as not containing O or 1.Therefore,it is of great significance to explore a new preprocessing method or prediction model of compositional data time series in theory.By combining fuzzy time series analysis with compositional data time series prediction,a kind of compositional data time series prediction method integrating fuzzy time series analysis is proposed in this paper.Firstly,information entropy measure is used to map the compositional data time series to the frame of real value sequence.Then,in the framework of fuzzy time series analysis,fuzzy C-means clustering is used to realize the division of domain associated to the transformed real value sequence and establish the corresponding relationship between fuzzy set and compositional data time series.Next,the first order fuzzy time series analysis model is used to predict the compositional data time series.Finally,the validity of the proposed prediction method is verified by an empirical analysis of the automobile sales data of an automobile company.

关 键 词：成分数据时间序列 预测 模糊时间序列 信息熵 对数比变换 

分 类 号：F830[经济管理—金融学] O212[理学—概率论与数理统计]