- Matrix differential calculus applied to multiple stationary time series and an extended Whittle formula for information matrices
- Linear Algebra and its Applications
- Volume | Issue number
- 430 | 2-3
- Pages (from-to)
- Number of pages
- Document type
- Faculty of Economics and Business (FEB)
Faculty of Science (FNWI)
- Amsterdam School of Economics Research Institute (ASE-RI)
Korteweg-de Vries Institute for Mathematics (KdVI)
The purpose of this paper is to set forth easily implementable expressions for the Fisher information matrix (FIM) of a Gaussian stationary vector autoregressive and moving average process with exogenous or input variables, a vector ARMAX or VARMAX process. The entries of the FIM are represented as circular integral expressions and can be computed by applying Cauchy’s residue theorem. An extension of the Whittle formula for the FIM of multiple time series processes is developed for VARMAX processes. It will be shown that the extended Whittle formula yields the FIM when a bivariate structure, consisting of the VARMAX process and the exogenous-input process, is considered. Consequently, the equivalence between a frequency and time domain representation of the FIM of VARMAX processes is established. In order to obtain the results presented in this paper, the differentiation techniques developed and used in [A. Klein, P. Spreij, An explicit expression for the Fisher information matrix of a multiple time series process, Linear Algebra Appl. 417 (2006) 140-149] are applied.
Keywords: Matrix differential calculus; Matrix polynomial; Fisher information matrix; VARMAX process; Whittle formula
Mathematical subject codes: 15A57; 15A69; 26B12; 62B10; 62H12
- go to publisher's site
If you believe that digital publication of certain material infringes any of your rights or (privacy) interests, please let the Library know, stating your reasons. In case of a legitimate complaint, the Library will make the material inaccessible and/or remove it from the website. Please Ask the Library, or send a letter to: Library of the University of Amsterdam, Secretariat, Singel 425, 1012 WP Amsterdam, The Netherlands. You will be contacted as soon as possible.