Testing for the change of the mean-reverting parameter of an autoregressive model with stationary Gaussian noise

Alexandre Brouste (1) , Chunhao Cai , Marius Soltane , Longmin Wang

1 LMM - Laboratoire Manceau de Mathématiques

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.

Mots clés: Autoregressive model; Change-point; Fractional Gaussian noise; Likelihood ratio test; Strong invariance principle

Domaines: Statistiques [math.ST]

Alexandre Brouste, Chunhao Cai, Marius Soltane, Longmin Wang. Testing for the change of the mean-reverting parameter of an autoregressive model with stationary Gaussian noise. Statistical Inference for Stochastic Processes, 2020, 23 (2), pp.301-318. ⟨10.1007/s11203-020-09217-1⟩. ⟨hal-03687258⟩