Computing the Exact Fisher Information Matrix of Periodic State-Space Models

Abstract

The purpose of this article is to develop algorithms for computing the exact Fisher information matrix of periodic time-varying state-space models. We first present a relatively simple recursive algorithm which computes the elements of the exact information matrix without involving numerical differentiation, since all required derivatives are analytically evaluated. The proposed algorithm extends the procedure due to Cavanaugh and Shumway (1996) to the periodic state-space framework. Exploiting the approach used in Klein et al. (2000), a second algorithm is proposed in order to obtain the exact information matrix as a whole instead of element by element. The algorithms are first developed in a general framework and then specialized to the case of a periodic Gaussian vector autoregressive moving-average (PVARMA) model.

Keywords:

• Chandrasekhar-type recursions
• Fisher Information matrix
• Periodic state-space models
• Periodic VARMA model

Mathematics Subject Classification:

• Primary 62M10
• Secondary 93E03

Acknowledgments

The author wishes to thank the referee for the critical comments and constructive suggestions which improved the article considerably.