|
Abstract:
|
In finance, meteorology, and many other fields, high-dimensional matrix-variate data are often observed overtime. Matrix-variate factor model is an effective dimension-reduction method that incorporates the structured interrelation between columns and rows. Exploration of the natural structures in loading matrices will improve performances of estimators and enhance interpretations of the estimated common factors. Thus we consider estimation and application of constrained and partially constrained factor model for matrix-variate time series. For estimation, we employ eigen-decomposition of non-negative definite matrices constructed from auto-covariance matrices at nonzero lags. We establish the asymptotic properties as the dimension and the number of constraints go to infinity with sample size; and propose likelihood ratio statistics to test the adequacy of factor constraints. We show that the rates of convergence of the constrained factor loading matrices are much faster than those of the conventional factor analysis. The proposed method and their asymptotic properties are further illustrated in a simulation study. An application to a corporate financial dataset is also reported.
|
