The Annals of Statistics

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

Richard A. Davis, Dawei Huang, and Yi-Ching Yao

Full-text: Open access


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.

Article information

Ann. Statist. Volume 23, Number 1 (1995), 282-304.

First available in Project Euclid: 11 April 2007

Permanent link to this document

Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier


Primary: 62F05: Asymptotic properties of tests
Secondary: 62M10: Time series, auto-correlation, regression, etc. [See also 91B84] 60G10: Stationary processes

Likelihood ratio statistic changepoint autoregressive process strong mixing


Davis, Richard A.; Huang, Dawei; Yao, Yi-Ching. Testing for a Change in the Parameter Values and Order of an Autoregressive Model. Ann. Statist. 23 (1995), no. 1, 282--304. doi:10.1214/aos/1176324468.

Export citation