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A note on the asymptotic eigenvalues and eigenvectors of the dispersion matrix of a second-order Stationary Process on a d-dimensional Lattice

Published online by Cambridge University Press:  14 July 2016

R. J. Martin
R. J. Martin*
Affiliation:
University of Sheffield
*
∗Postal address: Department of Probability and Statistics, The University, Sheffield S3 7RH, UK.
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Abstract

A sufficiently large finite second-order stationary time series process on a line has approximately the same eigenvalues and eigenvectors of its dispersion matrix as its counterpart on a circle. It is shown here that this result can be extended to second-order stationary processes on a d-dimensional lattice.

Keywords

FOURIER MATRIXLATTICE PROCESS
Type
Short Communications
Information
Journal of Applied Probability , Volume 23 , Issue 2 , June 1986 , pp. 529 - 535
Copyright
Copyright © Applied Probability Trust 1986 

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References

Bhansali, R. J. (1982) The evaluation of certain quadratic forms occurring in autoregressive model fitting. Ann. Statist. 10, 121–131.Google Scholar
Durbin, J. (1984) Present position and potential developments: some personal views. Time series analysis. J. R. Statist. Soc. A 147, 161–173.Google Scholar
Fuller, W. A. (1976) Introduction to Statistical Time Series. Wiley, New York.Google Scholar
Guyon, X. (1982) Parameter estimation for a stationary process on a d-dimensional lattice. Biometrika 69, 95–105.CrossRefGoogle Scholar
Mardia, K. V. and Marshall, R. J. (1984) Maximum likelihood estimation of models for residual covariance in spatial regression. Biometrika 71, 135–146.Google Scholar
Matheron, G. (1971) The Theory of Regionalised Variables and its Applications. Les Cahiers du Centre de Morphologie Mathematique. Fasc. No. 5, Fontainebleau.Google Scholar