Computation of the Fisher information matrix for SISO models

Closed form expressions and an algorithm for obtaining the Fisher information matrix of Gaussian single input single output (SISO) time series models are presented. It enables the computation of the asymptotic covariance matrix of maximum likelihood estimators of the parameters. The procedure makes use of the autocovariance function of one or more autoregressive processes. Under certain conditions, the SISO model can be a special case of a vector autoregressive moving average (ARMA) model, for which there is a method to evaluate the Fisher information matrix. That method is compared with the procedure described in the paper