Testing for the change of the mean-reverting parameter of an autoregressive model with stationary Gaussian noise
Résumé
The likelihood ratio test for a change in the mean-reverting parameter of a first order autore- gressive model with stationary Gaussian noise is considered. The test statistic converges in distribution to the Gumbel extreme value distribution under the null hypothesis of no change-point for a large class of covariance structures including long-memory processes as the fractional Gaussian noise.