Open Access
February, 1995 Testing for a Change in the Parameter Values and Order of an Autoregressive Model
Richard A. Davis, Dawei Huang, Yi-Ching Yao
Ann. Statist. 23(1): 282-304 (February, 1995). DOI: 10.1214/aos/1176324468

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.

Citation

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Richard A. Davis. Dawei Huang. Yi-Ching Yao. "Testing for a Change in the Parameter Values and Order of an Autoregressive Model." Ann. Statist. 23 (1) 282 - 304, February, 1995. https://doi.org/10.1214/aos/1176324468

Information

Published: February, 1995
First available in Project Euclid: 11 April 2007

zbMATH: 0822.62072
MathSciNet: MR1331669
Digital Object Identifier: 10.1214/aos/1176324468

Subjects:
Primary: 62F05
Secondary: 60G10 , 62M10

Keywords: autoregressive process , changepoint , likelihood ratio statistic , Strong mixing

Rights: Copyright © 1995 Institute of Mathematical Statistics

Vol.23 • No. 1 • February, 1995
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