Testing for a Change in the Parameter Values and Order of an Autoregressive Model
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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|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).|
|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 12:57|
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