Theory Of MARMA(p,q) Model And Its Application In International Trade

In many fields such as economy,finance,trade,industry and medicine,etc.,it is often necessary to comprehensively consider the interaction of multiple factors.For example,when predicting the change of one country's export volume to another country,it is highly related not only to the import volume,but also to the import and export volume of this country to other countries.But the current time series models that can only describe multi-dimensional situations can not meet the applications and needs,nor can it study multiple indicators of multiple variables from an overall perspective.Therefore,the matrix data time series model came into being.It makes the data more clear,and can greatly reduce the number of parameters.When the dimensions increase,it can reduce the dimensions obviously.Based on the existing research on matrix data time series model MARMA(p,q),firstly,this paper quotes the related concept,and expounds the definitions in detail.Through the equivalent transformation between VARMA(p,q)model and MARMA(p,q)model,with the help of the relevant theory of ARMA(p,q)model and the formula of matrix Kronecker product,this paper discuss the properties and identification method of the MARMA(p,q)model,proves the transfer form and reversal form of the model,and proposes the prediction method of the model.This paper discusses the least square estimation method of the model,and the gradient descent method is introduced to MARMA(p,q)model to reduce the dimension of parameter estimation,reduce the sum of squares of residuals and improve the estimation accuracy.In order to explore the mutual influence of import and export volume of international multilateral trade and predict the trade value,this paper uses the MARMA(p,q)model to make an empirical analysis of the monthly import and export trade data of China,the United States and the European Union from 2002 to 2019.The results show that the sum of squares of model residuals obtained by gradient descent method to estimate the coefficient matrix of MARMA(p,q)model is smaller and the method is better;this paper obtains the quantitative relationship of the change rate of import and export volume among the three economies,and the value next period of the sequence is predicted and analyzed.Using this model and method to analyze and predict the change of international trade can comprehensively consider the impact of trade exchanges among many countries.