- Construction of the exact Fisher information matrix of Gaussian time series models by means of matrix differential rules
- Linear Algebra and its Applications
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- Faculty of Economics and Business (FEB)
- Amsterdam School of Economics Research Institute (ASE-RI)
The Fisher information matrix is of fundamental importance for the analysis of parameter estimation of time series models. In this paper the exact information matrix of a multivariate Gaussian time series model expressed in state space form is derived. A computationally efficient procedure is used by applying matrix differential rules for the derivatives of a matrix function J=J(θ) with respect to its vector argument. An algorithm is given. It is sketched for the general state space structure without specifying a parametrization. It is then detailed for the vector autoregressive moving average (VARMA) model, with a given parametrization, where explicit recurrent relations are developed.
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