Computation of the Fisher information matrix for time series models

The Fisher information matrix is useful in time series modeling mainly because the significance of estimated parameters can also be derived from it. It can also be used in iterative procedures of parameter estimation. The paper is mainly concerned with algorithmic aspects related to the computation of that matrix either asymptotically or exactly. After a review of the literature on the subject, several recent methods are described and compared from the point of view of (a) complexity, (b) accuracy, and (c) the class of models for which they can be used.