Testing the Rank and Definiteness of Estimated Matrices with Applications to Factor, State-Space and ARMA Models
估计矩阵的秩与定性检验:因子、状态空间及 ARMA 应用
Consider any consistent, asymptotically normal estimate ǎ of an arbitrary rectangular or square matrix A. This article derives an explicit test for the rank of A and a related test of (semi) definiteness of A. Potential applications include testing for identification of structural models, testing for the number of state variables in state-space models (including tests for the order of autoregressive moving average (ARMA) processes), consumer demand analysis applications, and…