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Testing for a Change in the Parameter Values and Order of an Autoregressive Model

Davis, Richard A., Huang, Dawei, & Yao, Yi-Ching (1995) Testing for a Change in the Parameter Values and Order of an Autoregressive Model. The Annals of Statistics, 23(1), pp. 282-304.

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Abstract

The problem of testing whether or not a change has occurred in the parameter values and order of an autoregressive model is considered. It is shown that if the white noise in the AR model is weakly stationary with finite fourth moments, then under the null hypothesis of no changepoint, the normalized Gaussian likelihood ratio test statistic converges in distribution to the Gumbel extreme value distribution. An asymptotically distribution-free procedure for testing a change of either the coefficients in the AR model, the white noise variance or the order is also proposed. The asymptotic null distribution of this test is obtained under the assumption that the third moment of the noise is zero. The proofs of these results rely on Horvath's extension of Darling-Erdos' result for the maximum of the norm of a $k$-dimensional Ornstein-Uhlenbeck process and an almost sure approximation to partial sums of dependent random variables.

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49 citations in Web of Science®
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ID Code: 13131
Item Type: Journal Article
Additional Information: The contents of this journal can be freely accessed online via the journal's web page (see hypertext link).
Additional URLs:
DOI: 10.1214/aos/1176324468
ISSN: 0090-5364
Divisions: Past > QUT Faculties & Divisions > Faculty of Science and Technology
Copyright Owner: Copyright 1995 Institute of Mathematical Statistics
Deposited On: 25 Mar 2008
Last Modified: 09 Jun 2010 22:57

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