| High-dimensional matrix time series data arise from a variety of areas including finance,meteorology,visual detection,among others.It is of great significance to analyze matrix time series data and reveal its regularity for data analysis in many fields.In order to analysis matrix time series data,recent studies have considered the dynamic factor models.A direct way of applying dynamic factor model to matrixvalued time series analysis is to turn the matrix-valued data at each time point into a vector.However,vectorization usually ignores distinguishing information about row and column,which may lead to the loss of features and the difficulty of interpretation of the final results.Therefore,Wang et al proposed a pioneering matrix factor model in order to better study the properties of high-dimensional matrix time series data and predict the data,which can not only reduce the dimension of high-dimensional matrix time series data but also keep the time dependence of the matrix data.However,the existing parameter estimation methods can only estimate the load parameters of the matrix model proposed by Wang et al.In order to solve this problem,a quasi likelihood based two step estimation method is proposed in this paper,which can not only estimate the load matrix of the model but also estimate other parameters,including the variances of factors and noise and autoregressive coefficient.And the effectiveness of the estimation method is verified by simulation.Finally,the proposed method is applied to a dynamic network of international trade data from January 1982 to May 2020.By analyzing the dynamic network,it is found that this method can predict the dynamic network very well.The results show that the two-step estimation method is feasible and can be applied to practical problems. |
