An explicit expression for the Fisher information matrix of a multiple time series process. (English) Zbl 1092.62087
Summary: The principal result in this paper is concerned with the derivative of a vector with respect to a block vector or matrix. This is applied to the asymptotic Fisher information matrix (FIM) of a stationary vector autoregressive and moving average time series process (VARMA). Representations which can be used for computing the components of the FIM are then obtained. In a related paper of A. Klein [A generalization of Whittle’s formula for the information matrix of vector mixed time series. Linear Algebra Appl. 321, 197–208 (2000; Zbl 0966.62057)], the derivative is taken with respect to a vector. This is obtained by vectorizing the appropriate matrix products whereas in this paper the corresponding matrix products are left unchanged.
MSC:
| 62M10 | Time series, auto-correlation, regression, etc. in statistics (GARCH) |
| 26B12 | Calculus of vector functions |
| 15A69 | Multilinear algebra, tensor calculus |
Citations:
Zbl 0966.62057References:
| [1] | Klein, A., A generalization of Whittle’s formula for the information matrix of vector mixed time series, Linear Algebra Appl., 321, 197-208 (2000) · Zbl 0966.62057 |
| [2] | V. Peterka, P. Vidinčev, Rational-fraction approximation of transfer functions, First IFAC Symposium on Identification in Automatic Control Systems, Prague, 1967.; V. Peterka, P. Vidinčev, Rational-fraction approximation of transfer functions, First IFAC Symposium on Identification in Automatic Control Systems, Prague, 1967. |
| [3] | T. Söderström, Description of a program for integrating rational functions around the unit circle, Technical Report 8467R, Department of Technology, Uppsala University, 1984.; T. Söderström, Description of a program for integrating rational functions around the unit circle, Technical Report 8467R, Department of Technology, Uppsala University, 1984. |
| [4] | Whittle, P., The analysis of multiple stationary time series, J. Royal Statist. Soc. B., 15, 125-139 (1953) · Zbl 0053.41002 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
