Theory And Application Of The AR(p) Model Of Matrix Cross-Section Data Time Series

With the background of the rapid development of modern financial markets,markets have begun to appear diversified financial products.Since the advantages of diversified risks and stable returns,more and more peole have begun to focus on the overall return and the risk of the portfolio.However,the existing models are difficult to solve the probelm:the different attributes of the different objects co-change with time.Therefore,this paper proposes to construct a matrix cross-section data time series which characterize the model with this structure.First,this paper gives the definition and statistical characteristics of matrix cross-section data time series.Then the paper gives the definition of the most simple matrix cross-section data time series——stationay matrix cross-section data time series,and the estimation of the mean matrix and covariance matrix of stationay matrix cross-section data time series.Next,this paper takes the most popular times series——AR(p)model as an example,proposes AR(p)model of matrix cross-section data time series.And give the result of the model definition,the equivalence condition with the multivariate AR(p)model,the stationary conditions and parameter estimation.In order to describe the model structure better,this paper extends the model to the generalized AR(p)model of matrix cross-section data time series.Similarly,this paper makes a conclusion of the equivalence relation between this new model and the multivari-ate AR(p)model and gives the stationary conditions.Under the goal of minimizing the matrix norm,this paper gives the proposition that the model has a minimal value solu-tion,and the parameter estimation of the generalized AR(p)model of matrix cross-section data time series is given using some matrix theory like SVD method.Finally,this paper constructs multivariate AR(p)model and the AR(p)model of matrix cross-section data time series through actual data.It can be found that using the AR(p)model of matrix cross-section data time series makes the AIC value smaller,and can characterize the relationship between objects and attributes better.