Smooth Test For Disturbance Distribution In Vector Autoregressive Model And Application

As a widely used statistical analysis tool,time series analysis is a method of using the collected data to mine the regularity of things with time.What we usually consider is to analyze the time series of univariate.In the actual research,we need to study the object is usually multi-dimensional time series,how to extract the variation of multi-dimensional time series,through the establishment of model Its dynamic change rule is a problem that pays more attention to in today's society.Therefore,the time series analysis method has been extended from one dimension to multidimensional.As an analytical model describing the relationship between the changes of multivariable sequences,the vector autoregression model does not need to be based on economic theory.It can directly establish models from the data and is an unstructured model.Vector autoregressive model perturbation distribution needs to meet certain assumptions,in theory need to meet the multivariate normal distribution.If the vector autoregressive model perturbation distribution does not obey the multivariate normal distribution,then the statistical analysis based on the perturbation distribution is meaningless.From this we can see that it is very important to test the goodness of fit of the overall disturbance distribution.Therefore,it is significant to further study the test of disturbance distribution in vector autoregressive model and to propose a simple and effective method to test the goodness-of-fit of disturbance distribution.In this paper,we introduce a model based on multivariate time series analysis-vector autoregressive model,and describe a smooth test method for uniform spherical distribution.The smoothness test is applied to test the vestigial distribution of vector autoregressive model as multivariate normal distribution,and the actual data are analyzed and studied.The main work of this paper is as follows:(1)A smooth test of multivariate normal distribution for the disturbance distribution of vector autoregressive model is proposed.The simulated sub-site algorithm for multivariate normal distribution of perturbation and smooth test statistic algorithm are given.Combined with the collected 60 groups of real Four-dimensional data and the method of generating the opposite distribution,the use of MATLAB programming simulation test.(2)Empirical analysis based on the actual data,select the three variables of the growth rate of consumer price index,the year-on-year growth of broad money supply and the year-on-year growth of foreign exchange reserves,establish the vector autoregressive model,select the optimal lag order,Model stability test and integrity test are carried out,and the multivariate normality test is conducted on the disturbance distribution of the established vector autoregressive model.The vector autoregression model which is tested by model is used for extrapolation prediction.The prediction ellipsoid of the model and the impulse response analysis are given.