Computation of the exact information matrix of Gaussian time series with stationary random components

The paper presents an algorithm for efficient recursive computation of the Fisher information matrix of Gaussian time series whose random components are stationary, and whose means and covariances are functions of a parameter vector. The algorithm is first developed in a general framework and then specialized to the case of autoregressive moving average process, with possible additive white noise. The asymptotic behavior of the algorithm is explored and a termination criterion is derived.