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

In economic,industrial,biological,medical and other fields,there are time series of cross-sectional data composed of a plurality of multidimensional time series as a matrix,which is referred to as time series with matrix cross-section data.However,the existing time series model can only describe one-dimensional or multi-dimensional scenes,and it is impossible to study multiple properties of multiple variables as a whole.Therefore,this paper focuses on the matrix cross-section data time series and discuss more about the generalized AR(p)model of matrix cross-section data time series.First,this paper quotes the definition of matrix cross-section data time series,explained it's mean,covariance and stationarity and introduced the matrix cross-section white noise.Then,quotes the definition of the generalized AR(p)model of matrix cross-section data time series.By the skill of vectorize the matrix by column,this model can transform to VAR model.So,we can study this with the help of VAR model.Next,deduce the likelihood ratio,AIC,HQ and SC of the generalized AR(p)model of matrix cross-section data time series,by the conversion between it and VAR model.After that,to estimate the coefficient matrix of the model,in the process of minimizing matrix norms of residuals,this paper obtain the equations that the model coefficient matrix needs to satisfy Then,give the steps of numerically solving the coefficient matrix by the gradient descent algorithm.In the end,Under certain assumptions,according to the definition of matrix cross-section white noise,this paper obtain similarities between matrixe cross-section white noise test and one-dimensional time series white noise test.In terms of practice,this paper uses the relevant data of ICBC and ABC.At first,determine the order of the generalized AR(p)model of matrix cross-section data time series by VAR model.Then,use the gradient descent algorithm to estimate the coefficient matrix and build the model.Comparison of models established by existing coefficient matrix estimation methods,it can be found that the sum of the residuals of the model of the coefficient matrix estimated by the gradient descent algorithm is smaller.