The existence of Bartlett-Rajalakshman goodness of fitG-tests for multivariate autoregressive processes with finitely dependent residuals
- 1 April 1958
- journal article
- research article
- Published by Cambridge University Press (CUP) in Mathematical Proceedings of the Cambridge Philosophical Society
- Vol. 54 (2) , 225-232
- https://doi.org/10.1017/s0305004100033387
Abstract
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 theAiare 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.Keywords
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