Theoretical Research And Empirical Analysis Of Multi-dimensional Interval-valued Vector Autoregressive Time Series Models

Classical time series models play an important role in many fields.Since some data in practical uses are interval-valued rather that real-valued or vector-valued,it is necessary to study interval-valued time series models which are extensions of classical time series models.In this paper,we mainly study the multi-dimensional interval-valued stationary time series and the interval-valued vector autoregressive time series model.In the first chapter,we mainly recall the development of the theory of set-valued random variables,interval-valued linear regression models and interval-valued time series models.In the second chapter,we firstly recall the expectation and variance of one-dimensional interval-valued random variables.Then,we define the cross-covariance of generalized multidimensional interval-valued random vector and study the relative properties.In the third chapter,we use the expectation and cross-covariance of the multi-dimensional interval-valued random vectors to define the multi-dimensional interval-valued stationary time series,and give some properties of the cross-covariance.Then,The generalized multi-dimension interval-valued white noise is defined by the multi-dimension interval-valued stationary time series.Finally,the estimations of expectation and cross-covariance matrix are presented,both estimations are(asymptotically)unbiasedness.In the fourth chapter,the multi-dimensional interval-valued vector autoregressive(IVAR)model is introduced.Firstly,the IVAR(1)model is introduced.Then we discuss the IVAR(2)and the IVAR(p)models.Through transforming the IVAR(2)and IVAR(p)into the form of IVAR(1)model,we study the stability condition and moment equation of general models.Then,we use the information criterion,which based on the center and radius of the interval-valued observation data,to select the order of IVAR model.Next,we give the least squares estimation and Yule-Walker estimation methods,and prove the unbiasedness,consistency and asymptotic normality of the parameter estimations.After that,we give the K-NN prediction method base on the idea of clustering.Finally,the efficiency of parameter estimation is verified by a simulation study with IVAR(1)model.In the fifth chapter,we analyze the price of two stocks with IVAR(1)model.We calculate the parameter estimations with the least-squares estimation and Yule-Walker estimation methods.Then we use those estimations to give 3-step predictions respectively.Predictions shows the efficiency of the proposed model and approach.