Theoretical Research And Application Of Matrix Factor Analysis

High-dimensional matrix time series datasets are ubiquitous in real life,and are widely used in the monitoring of urban traffic status and air quality,social relationship networks,and dynamic import and export networks.The extensiveness of its data has attracted a large number of researchers to study and analyze high-dimensional matrix time series data sets.In recent years,researchers have established a time series model with a factor structure for high-dimensional matrix time series data,and the factor model of high-dimensional matrix time series data has been widely used in the correlation analysis of big data.focus on.Although most of the current related research work focuses on vector-valued time series data,research on matrix-valued or high-order tensor time series data sets is also becoming more common.Wang et al.proposed a factor model for matrix time series data.The model not only achieves significant dimensionality reduction,but also ensures the matrix structure and time dynamics of the data.Relevant scholars have done a lot of research on the estimation methods and related theories of this model.In this paper,for the factor model of matrix time series data proposed by Wang et al.,four kinds of assumptions that satisfy the identifiability of the model are proposed.By comparing the estimation method of Quasi-likelihood estimation method in this paper,the parameters are estimated and verified by simulation.the estimated validity.Finally,this paper applies the model to the Population flow network data in China,and studies the dynamic change law of its network structure.