摘要
研究集值多元时间序列的一些初步的理论,这为拓广经典的多元时间序列模型提供了理论基础.首先,基于集值理论,进一步提出集值向量、集值随机向量的定义,并给出集值随机向量的期望向量、交叉协方差阵与交叉相关阵的定义与性质.然后,在此基础上,给出集值多元时间序列的定义,并研究关于集值多元时间序列的平稳性,期望向量、交叉协方差阵和交叉相关阵的定义及性质,讨论平稳的集值多元时间序列的最优线性预测问题.最后,在集值多元时间序列的基础之上,讨论区间值多元时间序列,并建立区间值多元自回归模型.模拟研究与实证分析验证了该模型与所提出方法的合理性.
Some preliminaries for set-valued multivariate time series were studied,which provides a theoretical basis for extending the classical multivariate time series models.First,this paper introduced the definitions of set-valued vectors and set-valued random vectors based on the set-valued random variable theory.The definitions of expectation vectors,cross covariance matrixes and cross correlation matrixes were also given in this paper.Then,the set-valued multivariate time series was defined and the stationary property,expectation vectors,cross covariance matrixes and cross correlation matrixes of set-valued multivariate time series were discussed.Furthermore,the optimal linear forecast of stationary set-valued multivariate time series was studied.Finally,the interval-valued multivariate time series were discussed based on set-valued multivariate time series,and the interval-valued vector autoregressive model was built.Simulation study and real data analysis show the efficiency of the proposed model and approach.
作者
钟钰
李寿梅
章磊
ZHONG Yu;LI Shoumei;ZHANG Lei(College of Applied Sciences,Beijing University of Technology,Beijing 100124,China)
出处
《北京工业大学学报》
CAS
CSCD
北大核心
2020年第2期208-216,共9页
Journal of Beijing University of Technology
基金
国家自然科学基金资助项目(11571024)
关键词
集值随机向量
集值多元时间序列
交叉协方差阵
交叉相关阵
平稳性
区间值多元自回归模型
set-valued random vector
set-valued multivariate time series
cross-covariance matrix
cross-correlation matrix
stationary
interval-valued multivariate autoregressive model
