Computation of the exact information matrix of Gaussian dynamic regression time series models

In this paper, the computation of the exact Fisher information matrix of a large class of Gaussian time series models is considered. This class, which is often called the single-input-single-output (SISO) model, includes dynamic regression with autocorrelated errors and the transfer function model, with autoregressive moving average errors. The method is based on a combination of two computational procedures: recursions for the covariance matrix of the derivatives of the state vector with respect to the parameters, and the fast Kalman filter recursions used in the evaluation of the likelihood function. It is much faster than existing procedures. An expression for the asymptotic information matrix is also given.