The information matrix of multiple input single output time series models

Expressions are given for the information matrix of the parameters of the multiple-input single-output time series model for correlated and uncorrelated inputs, allowing lags between inputs. The model under consideration is a generalization of the multiple-regression model with autocorrelated errors, the transfer function model and the autoregressive moving average exogenous (ARMAX) model. The elements of the Fisher matrix are evaluated using algorithms developed for the univariate ARMA model.