Travail de recherche/Working paper
| Résumé : | In this paper the invertibility condition of the asymptotic Fisher information matrix of a controlled vector autoregressive moving average stationary process, VARMAX, is displayed in a theorem. It is shown that the Fisher information matrix of a VARMAX process becomes invertible if the VARMAX matrix polynomials have no common eigenvalue. Contrarily to what was mentioned previously in a VARMA framework, the reciprocal property is untrue. We make use of tensor Sylvester matrices since checking equality of the eigenvalues of matrix polynomials is most easily done in that way. A tensor Sylvester matrix is a block Sylvester matrix with blocks obtained by Kronecker products of the polynomial coefficients by an identity matrix, on the left for one polynomial and on the right for the other one. The results are illustrated by numerical computations. |
