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The existence of Bartlett-Rajalakshman goodness of fit G-tests for multivariate autoregressive processes with finitely dependent residuals

Published online by Cambridge University Press:  24 October 2008

A. M. Walker  and
D. V. Lindley
A. M. Walker
Affiliation:
Unit of BiometryOxford
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Extract

Bartlett and Rajalakshman (3) have derived two types of large sample goodness of fit tests for the hypothesis that a multivariate (or vector) time series {X(t)}, t = 0, ± 1, ± 2, …, is generated by a linear autoregressive process. This may be defined as the stationary solution of an equation of the form

where the Ai are square matrices such that the roots of the determinantal equation ‖ zp + A1zp−1 + … + Ap ‖ = 0 have moduli less than unity, and {U(t)} is a sequence of independent random vector variables with a common distribution.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 54 , Issue 2 , April 1958 , pp. 225 - 232
Copyright
Copyright © Cambridge Philosophical Society 1958

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References

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