Maximum Likelihood Identification of Structurally Constrained Covariances for Initial Condition Statistics

Maximum likelihood estimation of a constrained initial condition covariance matrix is treated in this paper. The associated cross-sectional observations are generated from non-identically distributed realizations of a linear dynamic system. The covariance matrix is constrained to both band-block structure and to general positive semi-definiteness. Necessary and sufficient conditions are derived for the local optimality of the constrained covariance estimate, and an algorithm for the numerical solution of the related optimality equations is indicated. An implementation of the EM method, which is useful in initializing the algorithm, is also presented for estimation in the band-block structurally constrained case.