Testing For A Change In The Parameter Values And Order Of An Autoregressive Model.
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Description
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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ID Code: | 13131 |
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Item Type: | Contribution to Journal (Journal Article) |
Refereed: | Yes |
Measurements or Duration: | 23 pages |
DOI: | 10.1214/aos/1176324468 |
ISSN: | 0090-5364 |
Pure ID: | 34605009 |
Divisions: | Past > QUT Faculties & Divisions > Faculty of Science and Technology Past > QUT Faculties & Divisions > Science & Engineering Faculty Current > Research Centres > Australian Research Centre for Aerospace Automation |
Copyright Owner: | Consult author(s) regarding copyright matters |
Copyright Statement: | This work is covered by copyright. Unless the document is being made available under a Creative Commons Licence, you must assume that re-use is limited to personal use and that permission from the copyright owner must be obtained for all other uses. If the document is available under a Creative Commons License (or other specified license) then refer to the Licence for details of permitted re-use. It is a condition of access that users recognise and abide by the legal requirements associated with these rights. If you believe that this work infringes copyright please provide details by email to qut.copyright@qut.edu.au |
Deposited On: | 25 Mar 2008 00:00 |
Last Modified: | 03 Mar 2024 17:16 |
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