- Tensor Sylvester matrices and the Fisher information matrix of VARMAX processes
- Linear Algebra and its Applications
- Volume | Issue number
- 432 | 8
- Pages (from-to)
- Document type
- Faculty of Economics and Business (FEB)
Faculty of Science (FNWI)
- Amsterdam School of Economics Research Institute (ASE-RI)
Korteweg-de Vries Institute for Mathematics (KdVI)
The purpose of this paper is to develop compact expressions for the Fisher information matrix (FIM) of a Gaussian stationary vector autoregressive and moving average process with exogenous or input variables, a vector ARMAX or VARMAX process. We develop a representation of the FIM based on multiple Sylvester matrices. An extension of this representation yields another one but in terms of tensor Sylvester matrices. In order to obtain the results presented in this paper, the approach used in [A. Klein, G. Mélard, P. Spreij, On the resultant property of the Fisher information matrix of a vector ARMA process, Linear Algebra Appl. 403 (2005) 291-313] is extended.
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